Princeton University

Workshop on Frontiers of Statistics

in Honour of

Professor Peter Bickel’s 65th Birthday

May 18 - 20, 2006, Princeton, USA

Table of Contents

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Biography of Peter J. Bickel . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Committees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Invited Speakers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Program Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Directions Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Abstracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Workshop Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Contents of Book “Frontiers of Statistics” . . . . . . . . . . . . . . . . . . . 38

Special Thanks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Acknowledgements

Sponsors

We gratefully acknowledge the generous financial support of :

Minerva Research Foundation

Bendheim Center for Finance, Princeton University

National Science Foundation

Department of Operations Research & Financial Engineering,

Princeton University

and academic support of:

Institute of Mathematical Statistics

International Indian Statistical Association

1

Background

The workshop intends to bring top and junior researchers together to define and ex-

pand the frontiers of statistics. It provides a focal venue for top and junior researchers to

gather, interact and present their new research findings, to discuss and outline emerging

problems in their fields, and to lay the groundwork for fruitful future collaborations. A

distinguished feature is that all topics are in core statistics with interactions with other dis-

ciplines such as biology, medicine, engineering, computer science, economics and finance.

Topics include: (1) Nonparametric inference and machine learning; (2) Longitudinal and

functional data analysis; (3) Time series, and financial econometrics; (4) Computational

biology and biostatistics; (5) MCMC, Bootstrap, and robust statistics; (6) Experimental

design and industrial engineering.

The workshop also serves advanced graduate students and young researchers looking

for new topics to work on and experienced researchers who hope to gain an overview of

contemporary developments in statistics.

The workshop is held on the occasion of the 65th birthday of Professor PeterJ. Bickel,

Professor of Statistics, University of California, Berkeley, one of the most celebrated statis-

ticians of our time. A book on the “Frontiers of Statistics” will soon be published based

on the topics presented on the workshop. The book will map the frontiers of the various

disciplines in statistics and provide useful references on the latest developments in each

subject. It will also be helpful to both new and experienced researchers who are willing

to gain a bird’s-eye view of the various frontiers of statistics, and published in celebration

of Professor Peter J. Bickel’s 65th birthday.

2

Biography of Peter J. Bickel

Peter J. Bickel

Peter Bickel has been a leading figure in the field of statistics

in the 43 years since he received his Ph.D. in Statistics at the

age of 22. He is widely recognized as one of the greatest statisti-

cians of our time in any metrics: breadth, depth and productivity.

He has made wide-ranging and far-reaching contributions to the

discipline of statistics. He has pioneered the research in many

statistical disciplines and has made fundamental contributions to

many areas in statistics. These include robust statistics, decision

theory, semiparametric modeling, bootstrap, nonparametric mod-

eling, machine learning, computational biology, and many other

areas (e.g. transportation and genomics) where statistics and

quantitative approaches play an important role. His exceptional

record of research accomplishment is evidenced by his exceptionally many publications in

the very top ranking journals in the field of statistics. His scientific findings have strongly

reshaped statistical thinking, methodological development, theoretical studies, and data

analysis. His research has strongly influenced the development of other quantitative dis-

ciplines such as engineering, economics, finance, computational biology, public health,

among others.

Bickel’s wide-ranging and far-reaching contributions to statistics have been signifi-

cantly recognized internationally by numerous awards and honors. These includes the

first recipient of The COPSS Presidents Award in 1980, and The Wald Lecturer in 1980.

His work has also been greatly recognized outside the statistical profession. These include

his John D. and Catherine T. MacArthur Foundation Fellowship in 1984, Guggenheim,

NATO, Miller Fellowships, and his election to the American Academy for Arts and Sciences

in 1985, the National Academy of Sciences in 1985, Royal Netherlands Academy of Arts

and Sciences in 1995. He was also honored the (UC-Berkeley) Chancellor’s distinguished

professor (1996-1999).

Professor Bickel is a strong professional leader. He has provided strong leadership

at all levels, from his enthusiastic administrative services to Berkeley as the department

chairman (76–79, 93–98), director of statistical laboratory (87-92), to a dean (twice) of the

Physical Sciences and many other important committees; from professional services such

as the President of The Institute of Mathematical Statistics (1980–1982), the president

of The Bernoulli Society (1991–1993), and the Board of Trustee of National Institute of

Statistics (1991 — ) to the national level such as various leading positions in the National

Academy of Sciences, National Research Council, Council of Scientific Advisors and the

American Association for the Advancement of Science.

3

Scientific Committee:

Jianqing Fan (Chair) Princeton University

Luisa Fernholz Princeton University

Hira Koul Michigan State university

Hans Mueller University of California at Davis

Vijay Nair University of Michigan

Ya’acov Ritov Hebrew University of Jerusalem

Jeff Wu Georgia Institute of Technology

Organizing Committee:

Jianqing Fan(Chair) Princeton University

Luisa T Fernholz Temple University

Heng Peng Princeton University

Chongqi Zhang Guangzhou University

Yazhen Wang University of Connecticut

Committee on Travel Support:

Luisa T. Fernholz (Chair) Princeton University

Jianqing Fan Princeton University

Liza Levina University of Michigan

Yijun Zuo Michigan State University

Yazhen Wang University of Connecticut

4

Invited speakers:

Yacine Ait-Sahalia Princeton University

Donald Andrews Yale University

Peter Buhlmann Swiss Federal Institute of Technology Zurich

Kjell Doksum University of California, Berkeley

David Donoho Stanford University

Ursula Gather University of Dortmund

Jayanta K. Ghosh Purdue University

Friedrich Goetze University of Bielefeld

Peter G. Hall The Australian National University

Haiyan Huang University of California at Berkeley

Jiming Jiang University of California, Davis

Hira Koul Michigan State University

Soumendra N. Lahiri Iowa State University

Elizaveta Levina University of Michigan

Jun Liu Harvard University

Regina Liu Rutgers University

Xiaoli Meng Harvard University

Stephan Morgenthaler EPFL Learning Center

Hans Muller University of California, Davis

Vijay Nair The University of Michigan

Byeong Park Seoul National University

Nancy Reid University of Toronto

John Rice University of California, Berkeley

Yaacov Ritov Israel Social Sciences Data Center

Anton Schick Binghamton University

Chris Sims Princeton University

David Tyler Rutgers University

Sara van der Geer Swiss Federal Institute of Technology Zurich

Mark van der Laan University of California, Berkeley

Willem van Zwet University of Leiden

Jane-Ling Wang University of California, Davis

Jon Wellner University of Washington

Yazhen Wang University of Connecticut

Jeff C. Wu Georgia Institute of Technology

Zhiliang Ying Columbia University

Chunming Zhang University of Wisconsin at Madison

Yijun Zuo Michigan State University

5

Program Overview

Thursday Friday Saturday

8:30-8:45 Registration

8:45-9:00 Opening Ceremony

9:00-9:30 Peter G. Hall Jun Liu Hira Koul John Rice

9:30-10:00 Peter Buhlmann Haiyan Huang Anton Sckick Jon Wellner

10:00-10:30 Sara van der Geer Zhiliang Ying Soumendra N. Lahiri Ureula Gather

10:30-11:00 Photo and Break Break Break

11:00-11:30 Willem Van Zwet Hans Muller Reginia Liu Jayanta K. Gosh

11:30-12:00 Nancy Reid Chunming Zhang Yijun Zuo Xiaoli Meng

12:00-12:30 Friedrich Goetze Byeong Park Jiming Jiang Jeff Wu

12:30-14:00 Lunch Lunch Lunch

14:00-14:30 Kjell Doksum David Donoho

14:30-15:00 Jane-Ling Wang David Tyler

15:00-15:30 Stephan Morgenthaler Yaacov Ritov

15:30-16:00 Break Break

16:00-16:30 Vijay Nair Chris Sims

16:30-17:00 Elizaveta Levina Yacine Ait-Sahalia

17:00-17:30 Mark van der Laan Donald Andrews

6

7

Program

May 17, 2006 (Wednesday)

19:30-21:30 Reception Palmer House

(http://www.princeton.edu/palmerhouse/)

Tel: 609-258-3715

Fax: 609-258-0526

May 18, 2006 (Thursday)

8:00-8:45 Registration F101∗

8:45-9:00 Opening Ceremony F101

Chair: Jianqing Fan

Invited Session

9:00-10:30 Chair: Don Fraser F101

9:00 Peter G. Hall

Some theory for classifiers in high-dimensional,

low sample size settings

9:30 Peter Buhlmann

Very high-dimensional data: prediction and

variable selection

10:00 Sara van der Geer

Oracle inequalities for the LASSO

10:30-11:00 Photo and Break

11:00-12:30 Chair: Ursula Gather F101

11:00 Willem van Zwet

An expansion for a discrete non-lattice

distribution

11:30 Nancy Reid

Applied Asymptotics

12:00 Friedrich Goetze

Edgeworth Approximations for

Symmetric Statistics

8

12:30-14:00 Lunch (Friend Convocation Room)

14:00-15:30 Chair: Luisa Fernholz F101

14:00 Kjell Doksum

Powerful Choices: Variable and Tuning

Constant Selection in Nonparametric

Regression based on Power

14:30 Jane-Ling Wang

Flexible Approaches to Model Survival

and Longitudinal Data Jointly

15:00 Stephan Morgenthaler

Smoothing Large Tables

15:30-16:00 Break

16:00-17:30 Chair: David Blei F101

16:00 Vijay Nair

Statistical Inverse Problems in Active Network

Tomography

16:30 Elizaveta Levina

Detection in Wireless Sensor Networks

17:00 Mark van der Laan

Estimating function based cross-validation

End of day 1

∗Friend 101

9

Program

May 19, 2006 (Friday)

8:45-9:00 Registration F006∗

Parallel Invited Sessions

9:00-10:30 Chair: Julian Faraway F006

9:00 Jun Liu

Bayesian Methods in Haplotype Inference

and Disease Mapping

9:30 Haiyan Huang

A statistical framework to infer functional

gene associations from multiple biologically

dependent microarray experiments

10:00 Zhiliang Ying

Semiparametric mixed effects models for

duration and longitudinal data

9:00-10:30 Chair: Run-ze Li F004∗∗

9:00 Hira Koul

Goodness-of-fit testing in interval

censoring case 1

9:30 Anton Sckick

Efficient estimators for times series

10:00 Soumendra N. Lahiri

Edgeworth expansions for sums of

block-variables under weak dependence

10:30-11:00 Break

11:00-12:30 Chair: Richard Samworth F006

11:00 Hans Muller

Functional Variance

11:30 Chunming Zhang

Spatially Adaptive Functional Linear

Regression with Functional Smooth Lasso

12:00 Byeong Park

Estimation and Testing for Varying

10

Coefficients in Additive Models with

Marginal Integration

11:00-12:30 Chair: Miriam Donoho F004

11:00 Reginia Liu

Mining Massive Text Data: Classification,

Construction of Tracking Statistics and

Inference under Misclassification

11:30 Yijun Zuo

Multi-Dimensional Trimming Based on

Data Depth

12:00 Jiming Jiang

Fence Methods: Another Look at Model Selection

12:30-14:00 Lunch(Friend Convocation Room)

Invited Session

14:00-15:30 Chair: Stephan Morgenthaler FCR∗∗∗

14:00 David Donoho

Sparsity in Inference: past trends,

future promise

14:30 David Tyler

Invariant coordinate selection (ICS):

A robust statistical perspective on

independent component analysis (ICA)

15:00 Yaacov Ritov

Some remarks on non-linear

dimension reduction

15:30-16:00 Break

16:00-17:30 Chair: Yazhen Wang FCR

16:00 Chris Sims

Bayesian Inference in Central Banks: Recent

Developments in Monetary Policy Modeling

16:30 Yacine Ait-Sahalia

Likelihood Inference for Diffusions

17:00 Donald Andrews

The Limit of Finite Sample Size and a

Problem with Subsampling

End of day 2

∗Friend 006 ∗∗Friend 004 ∗∗∗Friend Convocation Room

11

Program

May 20, 2006 (Saturday)

8:45-9:00 Registration FCR

Invited Sessions

9:00-10:30 Chair: Anirban Dasgupta FCR

9:00 John Rice

Multiple Testing in Astronomy

9:30 Jon Wellner

Goodness of fit via phi-divergences:

a new family of test statistics

10:00 Ursula Gather

Methods of robust online signal

extraction and applications

10:30-11:00 Break

11:00-12:30 Chair: Zhezhen Jin FCR

11:00 Jayanta K. Gosh

Convergence and Consistency of

Newton’s Algorithm for Estimating a

Mixing Distribution

11:30 Xiaoli Meng

Statistical physics and statistical

computing: A critical link– estimating

criticality via perfect sampling

12:00 Jeff Wu

Bayesian Hierarchical Modeling for

Integrating Low-accuracy and

High-accuracy Experiments

12:30-14:00 Lunch(Friend Convocation Room)

End of day 3

12

Abstracts

13

Likelihood Inference for Diffusions

Yacine Ait-Sahalia

Bendheim Center for Finance Princeton University, Princeton University

This talk surveys recent results on closed form likelihood expansions for discretely

sampled diffusions. One major impediment to both theoretical modeling and empirical

work with continuous-time models is the fact that in most cases little can be said about

the implications of the instantaneous dynamics for longer time intervals. One cannot in

general characterize in closed form an object as simple, yet fundamental for everything

from prediction to estimation and derivative pricing, as the conditional density of the

process, also known as the transition function of the process. I will describe a method

which produces accurate approximations in closed form to the transition function of an

arbitrary multivariate diffusion. I will then show a connection between this method and

saddlepoint approximations and provide examples. Next, I will discuss inference using this

method when the state vector is only partially observed, as in stochastic volatility or term

structure models. Finally, I will outline the use of this method in specification testing and

sketch derivative pricing applications.

The Limit of Finite Sample Size and a Problem withSubsampling

Donald W.K. Andrews

Department Economics, Yale University

This paper considers tests and confidence intervals based on a test statistic that has

a limit distribution that is discontinuous in a nuisance parameter or the parameter of

interest. The paper shows that standard fixed critical value (FCV) tests and subsample

tests often have asymptotic size—defined as the limit of the finite sample size—that is

greater than the nominal level of the test. We determine precisely the asymptotic size of

such tests under a general set of high-level conditions that are relatively easy to verify.

Often the asymptotic size is determined by a sequence of parameter values that approach

the point of discontinuity of the asymptotic distribution. The problem is not a small

sample problem. For every sample size, there can be parameter values for which the test

over-rejects the null hypothesis. Analogous results hold for confidence intervals.

We introduce a hybrid subsample/FCV test that alleviates the problem of over-rejection

asymptotically and in some cases eliminates it. In addition, we introduce size-corrections

to the FCV, subsample, and hybrid tests that eliminate over-rejection asymptotically. In

some examples, these size corrections are computationally challenging or intractable. In

other examples, they are feasible. This is joint work with Patrik Guggenberger.

14

Very High-dimensional Data: Prediction and VariableSelection

Peter Buhlmann

Swiss Federal Institute of Technology Zurich

We consider problems where the number of predictor variables p is much larger than

sample size n, i.e. function, the Lasso or also boosting algorithms have been shown to

be asymptotically consistent and both of them often exhibit very good empirical perfor-

mance. However, the problem of variable selection is much more subtle and difficult than

prediction.

We will discuss theoretical and practical potential and limitations of the Lasso and

boosting for variable selection, and we will present powerful improvements. The talk is a

special birthday tour for Peter Bickel: from ”Relaxed Lasso” over ”Sparse Boosting” to

completely different ideas from the ”PC algorithm” in graphical modeling. The methods

are used for two problems in computational biology: (i) alternative splicing using single-

gene libraries; and (ii) short motif modeling for splice site detection.

Powerful Choices: Variable and Tuning Constant Selectionin Nonparametric Regression based on Power

Kjell Doksum

Department of Statistics, University of California, Berkeley

This paper considers nonparametric multiple regression procedures for analyzing the

relationship between a response variable and a vector of covariates. It uses an approach

which handles the dilemma that with high dimensional data the sparsity of data in re-

gions of the sample space makes estimation of nonparametric curves and surfaces virtually

impossible. This is accomplished by abandoning the goal of trying to estimate true under-

lying curves and instead estimating measures of dependence that can determine important

relationships between variables. These dependence measures are based on local parametric

fits on subsets of the covariate space that vary in both dimension and size within each

dimension. The subset which maximizes a signal to noise ratio is chosen. The signal is a

local estimate of a dependence parameter which depends on the subset size, and the noise

is an estimate of the standard error (SE) of the estimated signal. This approach of choos-

ing the window size to maximize a signal to noise ratio lifts the curse of dimensionality

because for regions with sparsity of data the SE is very large. For contigious Pitman al-

ternatives it corresponds to asymptotically maximizing the probability of correctly finding

relationships between covariates and a response, that is, maximizing asymptotic power. It

is shown that within a selected dimension, the bandwidths of the optimally selected subset

15

do not tend to zero as the sample size n grows except for alternatives where the length of

the intervals where the alternative differs from the hypothesis tends to zero as n grows.

One of the dimension reduction algorithms is used together with MARS and GUIDE and

is shown to improve their performance. This is joint work with Chad Schafer, Shijie Tang

and Kam Tsui.

Sparsity in Inference: Past Trends, Future Promise

David Donoho

Statistics Department, Stanford University

Suppose we have to estimate a large number of parameters, most of which are zero or

negligible and some of which are important or significant; but we don’t know in advance

which parameters are likely to be negligible and which’are likely to be important. This

important problem in some sense spans large swaths of applied statistics, from regression

model building to gene association studies.

I’ll discuss some of Peter Bickel’s early work related to this problem, and how the

problem has grown and mutated over the years. At this point, it’s a problem with truly

vast implications, having applications throughout science and technology, with lots of

challenging mathematics and surprising applications.

Methods of Robust Online Signal Extraction andApplications

Ursula Gather

Department of Statistics, University of Dortmund

We discuss filtering procedures for robust extraction of a signal from noisy time series.

These methods can e.g. be applied to online observations of vital parameters which are

acquired by clinical information systems for critically ill patients. Multivariate time series

from online monitoring exhibit trends, abrupt level changes and large spikes (outliers)

as well as periods of relative stability. Also, the measurements are overlaid with a high

level of noise and among the variables strong dynamic dependencies are found (Gather et

al. (2002)). The challenge is to develop methods that allow a fast and reliable denoising

of these time series. Noise and artifacts are to be separated from structural patterns of

relevance.

Standard approaches to univariate signal extraction are moving averages and (univari-

ate) running medians, but they have shortcomings when outliers or trends occur. Review-

ing and extending recent work we present new methods for robust online signal extraction

and discuss their merits for preserving trends, abrupt shifts and extremes and for the

removal of spikes (Davies, Fried, Gather (2004)). Our robust regression moving window

16

methods are applicable even in real time because of increased computational power and

fast algorithms (Bernholt and Fried (2003)).

In multivariate robust signal extraction efficiency is lost if the error terms of the vari-

ables are highly correlated since generalizing robust univariate regression methods does not

result in affine equivariant procedures. Multivariate affine equivariant regression methods

with high breakdown, as e. g. MCD-regression (Rousseeuw et al. (2004)), more over

assume that the data are in general position. For discrete data in short time windows this

is however often not the case.

We therefore propose new procedures for multivariate signal extraction, which offer

fast and robust signal extraction, good efficiency properties and which can be used for

discretely measured data with low variability as well as in situations with many outliers.

Convergence and Consistency of Newton’s Algorithm forEstimating a Mixing Distribution

Jayanta K. Ghosh

Department of Statistics, Purdue University

In recent years Michael Newton has proposed an algorithmic estimate of a mixing

distribution, which is computationally efficient. We prove its convergence and consistency

under rather strong conditions. The consistency result is new. A proof of convergence

given earlier under same conditions by Newton is shown to be incomplete and not easily

rectifiable. We study various other aspects of the estimate and compare it with the Bayes

estimate based on Dirichlet mixtures. This is joint work with Surya Tokdar.

Edgeworth Approximations for Symmetric Statistics

Friedrich Goetze

Department of Mathematics, University of Bielefeld

We shall describe conditions, such that Edgeworth approximations up to an error

o(N−1) hold for a general class of asymptotical linear symmetric statistics in N indepen-

dent observations, which admits a regular stochastic Hoeffding expansion. The conditions

involve Cramer’s condition of smoothness for the linear term and some covariance type

conditions for the second order term. The results are joint work with M. Bloznelis and

extend previous work by P. Bickel, V. Bentkus, W. van Zwet and the author. They are

based on new analytical and combinatorial techniques. Connections with approximation

results in Probability and Number Theory for related degenerate U -statistics, and their

dimension dependence will be discussed as well.

17

Some Theory for Classifiers in High-dimensional, LowSample Size Settings

Peter Hall

Centre for Mathematics and its Applications, Mathematical Sciences Institute,

Australian National University

A large class of distance-based classifiers is defined, and their performance addressed

using theoretical arguments based on letting dimension diverge as sample size is kept

fixed. Particular attention is paid to the use of truncation, to heighten sensitivity of the

classifiers in cases of data sparsity. It is shown that in that setting, truncated distance-

based classifiers can perform well when differences between distributions are detectable

but not estimable. They do not do quite as well as classifiers based on Donoho and

Jin’s higher-criticism methods, although they are more robust against assumptions about

distribution type and component relationships. However, the robustness of higher criticism

can be increased by using methods based thresholding, as well as empirical approaches.

A Statistical Framework to Infer Functional GeneAssociations from Multiple Biologically Dependent

Microarray Experiments

Haiyan Huang

Department of Statistics, University of California, Berkeley

Microarray data from an increasing number of biologically interrelated and interde-

pendent experiments now allow more complete portrayals of functional gene relationships

involved in biological processes. However, in the current integrative analyses of microarray

data, an important practical issue is widely ignored: the existence of dependencies among

gene expressions across biologically related experiments. When not accounted for, these

dependencies (due to either similar intrinsic conditions or relevant external perturbations

among the experiments) can result in inaccurate inferences of functional gene associa-

tions, and hence incorrect biological conclusions. To address this fundamental problem,

we propose a new measure, Knorm correlation, to quantify functional gene associations

in the presence of such experimental dependencies. Our intuitive strategy is to reduce

the experimental dependencies before estimating gene correlations. The statistical model

underlying Knorm correlation is a multivariate normal distribution characterized by a

Kronecker product dependency structure. This unique structure maintains the same ex-

perimental correlations across genes and the same gene correlations across experiments.

The proposed measure simplifies to the Pearson coefficient when experiments are uncor-

related. Applications to simulation studies and to two real datasets (on yeast and human

18

genes) demonstrate the success of Knorm correlation, and also the adverse impact of exper-

imental dependencies on gene associations using Pearson coefficients. Knorm correlation is

expected to greatly improve the accuracy of biological inferences made from experiments

currently (and incorrectly) assumed to be uncorrelated.

This is a joint work with Melinda Teng and Xianghong Zhou.

Fence Methods: Another Look at Model Selection

Jiming Jiang

Department of Statistics, University of California, Davis

Many model search strategies involve trading off model fit with model complexity in a

penalized goodness of fit measure. Asymptotic properties for these types of procedures in

settings like linear regression and ARMA time series have been studied. Yet, such strate-

gies do not always translate into good finite sample performance. The issue is typically

one of the procedure being overly sensitive to the setting of penalty parameters, which are

required to be increasing functions of sample size. Furthermore, these strategies do not

generalize naturally to more complex models, such as those for modeling clustered data

or those that involve adaptive estimation. In these cases, penalties and model complexity

may not be naturally defined.

We introduce a new class of model selection strategies known as fence methods. The

general idea involves a procedure to isolate a subgroup of what are known as correct

models (of which the optimal model is a member). This is accomplished by constructing

a statistical fence, or barrier, to carefully eliminate incorrect models. Once the fence is

constructed, the optimal model will be selected among the correct models (those within the

fence) according to simplicity of the models. We describe a variety of fence methods, based

on the same principle but applied to different situations. These include regression, least

angle regression, linear mixed models for clustered and non-clustered data, generalized

linear mixed models for clustered and non-clustered data, and time series models. We

show the broad applicability of fence methods to all of these areas by giving a number

of examples, each supported by simulation results or real-life data analyses. In terms of

theoretical development, we give sufficient conditions for consistency of fence, a desirable

property for a good model selection procedure.

This work is joint with J. Sunil Rao, Zhonghua Gu and Thuan Nguyen.

19

Goodness-of-fit Testing in Interval Censoring Case 1

Hira L. Koul

Department of Statistics and Probability, Michigan State University

In the interval censoring case 1, an event occurrence time is unobservable, but one ob-

serves an inspection time and whether the event has occurred prior to this time or not. The

focus here is to provide tests of goodness-of-fit hypothesis pertaining to the distribution

of the event occurrence time. The proposed tests are based on certain marked empirical

processes for testing a simple hypothesis and their martingale transforms. These tests are

asymptotically distribution-free, consistent against a large class of fixed alternatives and

have nontrivial asymptotic power against a large class of local alternatives.

Edgeworth Expansions for Sums of Block-variables underWeak Dependence

Soumendra N. Lahiri

Department of Statistics, Iowa State University

Let {Xi}∞i=−∞ be a sequence of random vectors and let Yin = fin(Xi,l) be zero mean

block-variableswhere Xi,l = (Xi, . . . ,Xi+l−1), i ≥ 1 are overlapping blocks of length ℓ and

where fin are Borel measurable functions. This paper establishes valid joint asymptotic

expansions of general orders for the joint distribution of the sums∑n

i=1Xi and∑n

i=1 Yin

under weak dependence conditions on the sequence {Xi}∞i=−∞ when the block length ℓ

grows to infinity. In contrast to the classical Edgeworth expansion results where the terms

in the expansions are given by powers of n−1/2, the expansions derived here are mixtures

of two series, one in powers of n−1/2 while the other in powers of [nl ]−1/2. Applications

of the expansions to studentized statistics and to block bootstrap methods for time series

data are given.

Detection in Wireless Sensor Networks

Elizaveta Levina

Department of Statistics, The University of Michigan

Wireless sensor networks are becoming more widely available for use in various appli-

cations, such as intruder detection and ecological monitoring. The basic issues in sensor

networks (detection, estimation, design) are statistical but little work in this area has been

20

done by statisticians. I will give a brief overview of the main problems and then focus

on a local-vote decision algorithm we developed for target detection by a wireless sensor

network. Sensors acquire measurements corrupted by noise, make individual decisions,

correct their decisions after consulting the neighboring sensors, and then a collective deci-

sion is made by the network. Related local methods have been proposed by the engineers

but no theoretical performance guarantees were available. We give an explicit formula for

the decision threshold for a given false alarm rate, based on limit theorems for weakly

dependent random fields. We also show that, for a fixed false alarm rate, the local-vote

correction significantly improves target detection rate.

Joint work with George Michailidis and Natallia Katenka.

Bayesian Methods in Haplotype Inference and DiseaseMapping

Jun Liu

Department of Statistics, Harvard University

Haplotypes provide complete information of inheritance, which are very useful in pop-

ulation genetics and association studies. Since experimentally determining haplotype data

is expensive, much effort has been devoted to develop computational tools for inferring

haplotypes from genotype data. I will present a few Bayesian and semi-Bayesian models

that have been formulated over the past few years for this task, including new hierarchical

Bayes model developed in our group that incorporates the coalescence effect in a prior

distribution. The prediction accuracy of the new method is uniformly improved compared

to existing methods such as HAPLOTYER and PHASE.

I will further discuss a Bayesian approach in detecting multi-locus interactions (epista-

sis) for case-control association studies. Existing methods are either of low power or com-

putationally infeasible when facing of a large number of markers. Using MCMC sampling

techniques, the method can efficiently detect interactions among thousands of markers.

Using simulation results, I will discuss the power of our approach and the importance to

consider epistasis in association mapping.

Based on joint work with Yu Zhang and Tim Niu.

21

Mining Massive Text Data: Classification, Construction ofTracking Statistics and Inference under Misclassification

Regina Liu

Department of Statistics, Rutgers University

We present a systematic data mining procedure for exploring large free-style text

datasets to discover useful features and develop tracking statistics (often referred to as

performance measures or risk indicators). The procedure includes text classification, con-

struction of tracking statistics, inference under error measurements and risk analysis. The

main difficulty in deriving this inference scheme is the accounting for misclassification

errors, for which we propose two types of approaches: “plug-in” and “projection” meth-

ods. We also consider the bootstrap calibration for fine tuning. Finally, as an illustrative

example, the proposed data mining procedure is applied to analyzing an aviation safety

report repository from the FAA to show its utility in aviation risk management or general

decision-support systems.

Although most illustrations here are drawn from aviation safety data, the proposed

data mining procedure applies to many other domains, including, for example, mining

free-style medical reports for tracking possible disease outbreaks.

This is joint work with Daniel Jeske, Department of Statistics, UC Riverside.

Statistical Physics and Statistical Computing: A CriticalLink– Estimating Criticality via Perfect Sampling

Xiao-Li Meng

Department of Statistics, Harvard University

This talk is based on the following chapter, jointly written with James Servidea of U.S.

Department of Defense, in the volume dedicated to Professor Peter Bickel: “The main

purpose of this chapter is to demonstrate the fruitfulness of cross-fertilization between

statistical physics and statistical computation, by focusing on the celebrated Swendsen-

Wang algorithm for the Ising model and its recent perfect sampling implementation by

Mark Huber. In particular, by introducing Hellinger derivative as a measure of instanta-

neous changes of distributions, we provide probabilistic insight into the algorithm’s critical

slowing down at the phase transition point. We show that at or near the phase transition,

an infinitesimal change in the temperature parameter of the Ising model causes an as-

tronomical shift in the underlying state distribution. This finding suggests an interesting

conjecture linking the critical slowing down in coupling time with the grave instability of

the system as characterized by the Hellinger derivative (or equivalently, by Fisher infor-

mation). It also suggests that we can approximate the critical point of the Ising model, a

22

physics quantity, by monitoring the coupling time of Huber’s bounding chain algorithm,

an algorithmic quantity. This finding might provide an alternative way of approximating

criticality of thermodynamic systems, which is typically intractable analytically. We also

speculate that whether we can turn perfect sampling from a pet pony into a workhorse

for general scientific computation may depend critically on how successful we can engage,

in its development, researchers from statistical physics and related scientific fields.”

Smoothing Large Tables

Stephan Morgenthaler

EPFL Learning Center

Methods to smooth large tables are described. Such smoothing problems are of interest

in many scientific contexts and with a variety of objectives in mind. One may want to

interpolate the table entries, or to quantify the differences between rows and columns, or

to classify rows and columns into homogeneous subgroups, or to find the best rows and

columns, or some other objective. Fisher’s ANOVA, which can be computed by sweeping

row means and column means from the table, assigns a single effect to each row and

each column and was originally invented for tables of low dimension. The singular value

decomposition of the table offers an alternative single effects approximation. In both cases,

the smoothed row traces, that is the plot of the row entries against the row effects, are

straight lines.

More general table smoothers are obtained by using more flexible traces. Some of

the difficulties with this approach are discussed, among them the choice of row and col-

umn variables replacing the single effects from above, the parsimonious choice of trace

parameters, the classification of traces, and the transformation of table entries.

Functional Variance

Hans-Georg Muller

Department of Statistics, University of California, Davis

Functional data consist of an observed sample of smooth random trajectories. A key

tool for the analysis of such data is a representation in terms of eigenfunctions of the

autocovariance operator of the underlying stochastic process and the associated functional

principal components. In some applications the information of interest resides not in

the observed smooth random trajectories themselves but rather in the additive noise.

Assuming the noise is composed of a white noise component and a smooth random process

component, we refer to the latter as the functional variance process. This process can

23

then be decomposed in terms of its eigenfunctions. Methods to estimate eigenfunctions

and functional principal component scores for the functional variance process are based on

residuals obtained in an initial smoothing step, applied to the original data. We discuss

asymptotic justifications and applications. (joint work with U. Stadtmuller and F. Yao).

Statistical Inverse Problems in Active Network Tomography

Vijay Nair

Department of Statistics, Department of Industrial & Operations Engineering,

University of Michigan, Ann Arbor

The term network tomography, first introduced in Vardi (1996), characterizes two

classes of large-scale inverse problems that arise in the modeling and analysis of computer

and communications networks. This talk will deal with active network tomography where

the goal is to recover link-level quality of service parameters, such as packet loss rates and

delay distributions, from end-to-end path-level measurements. Internet service providers

use this to characterize network performance and to monitor service quality. We will

provide a review of recent developments, including the design of probing experiments,

inference for loss rates and delay distributions, and applications to network monitoring.

This is joint work with George Michailidis, Earl Lawrence, Bowei Xi, and Xiaodong Yang.

Estimation and Testing for Varying Coefficients in AdditiveModels with Marginal Integration

Byeong Park

Department of Statistics, Seoul National University

We propose marginal integration estimation and testing methods for the coefficients of

varying coefficient multivariate regression model. Asymptotic distribution theory is devel-

oped for the estimation method which enjoys the same rate of convergence as univariate

function estimation. For the test statistic, asymptotic normal theory is established. These

theoretical results are derived under the fairly general conditions of absolute regularity

(β-mixing). Application of the test procedure to the West German real GNP data reveals

that a partially linear varying coefficient model is best parsimonious in fitting the data

dynamics, a fact that is also confirmed with residual diagnostics.

24

Applied Asymptotics

Nancy Reid

Department of Statistics, University of Toronto

The theory of higher order asymptotics provides quite accurate approximations for

a large number of parametric models. However, the details of the theory are somewhat

complicated, and perhaps for that reason the methods are not used as often as they might

be. I will outline some ’case studies’ where improved approximation is readily implemented

and illustrate the effects on the resulting inference. I will suggest areas where further

research is needed.

Multiple Testing in Astronomy

John Rice

Department of Statistics, University of California, Berkeley

Suppose that a very large number of independent null hypotheses are tested, almost

all of which are true. How can the proportion of false null hypotheses be estimated? For

motivation, I will discuss the Taiwanese-American Occultation Survey, and will explain

how this question arises. I will then present some recent results.

Some Remarks on Non-linear Dimension Reduction

Ya’acov Ritov

Israel Social Sciences Data Center

We remark on the possibility of a well defined dimension reduction. We consider a

model in which the data is distributed on a manifold. We present an algorithm for gener-

ating a global map of data to a lower dimensional space, minimizing the local structure of

the manifold. We remark on the importance on estimating the manifold structure when

the main concern is estimating a regression function.

Efficient Estimators for Times Series

Anton Schick

Department of Mathematical Sciences, Binghamton University

I illustrate several recent results on efficient estimation for semiparametric time series

models with a simple class of models: first-order nonlinear autoregression with indepen-

dent innovations. In particular I consider estimation of the autoregression parameter, the

innovation distribution, conditional expectations, the stationary distribution, the station-

ary density, and higher-order transition densities.

25

Bayesian Inference in Central Banks: Recent Developmentsin Monetary Policy Modeling

Christopher A. Sims

Department of Economics, Princeton University

In the 1950’s and 60’s, large-scale econometric models, grounded in an elegant the-

ory of inference initiated by Trygve Haavelmo, began to be widely used by policy-making

instituions. While the models remained in use, their grounding in a theory of inference

almost completely disappeared by 2000. In the last few years, there has been research ac-

tivity in many central banks aimed at producing models grounded in a Bayesian approach

to inference and using modern computational approaches to posterior simulation. This

talk summarizes the history and describes the methods and results driving the current

research.

Invariant Coordinate Selection (ICS): A Robust StatisticalPerspective on Independent Component Analysis (ICA)

David E. Tyler

Department of Statistics, Rutgers University

In many disciplines, independent component analysis (ICA) has become a popular

method for analyzing multivariate data. Independent component analysis typically as-

sumes the observe data Y ∈ ℜp is generated by a nonsingular affine transformaton of inde-

pendent components, i.e. Y = AZ, where A is a nonsingular matrix and Z = (Z1, . . . , Zp)′

consists of independent variables Z1, . . . , Zp. The objective is to then estimate A and hence

recover Z. Approaches for recovering Z have often been successful in exploring multivari-

ate data in general, i.e. in cases where the ICA model may not be hold. The purpose

of this talk is to provide some understanding as to why independent component analysis

may work well as a general multivariate method. In particular, without reference to the

ICA model, it can be noted that for some methods the recovered Z can be viewed as affine

invariant coordinates. That is, if we transform Y → Y∗ = BY + b for any nonsingular

Y, then Z∗ = ∆Z + c, where ∆ is a nonsingular diagonal matrix. In other words, the

standardized versions of the components Zj and Z∗j are the same. Hence, the terminology

invariant coordinate selection (ICS).

Consequently, this leads to the development of a wide class of affine equivariant co-

ordinatewise methods for multivariate data. Some methods to be discussed are affine

equivariant principal components, robust estimates of multivariate location and scatter,

affine invariant multivariate nonparametric tests, affine invariant multivariate distribution

functions, and affine invariant coordinate plots. The affine equivariant principal compo-

26

nents and the corresponding affine invariant coordinate plots can be regarded in a sense as

projection pursuit without the pursuit. Several examples are given to illustrate the utility

of the proposed methods.

Oracle Inequalities for the LASSO

Sara van de Geer

Seminar fuer Statistik, ETH Zuerich

We consider the LASSO penalty for general M-estimators. Examples include logistic

regression, quantile regression, log-density estimation, and boosting with for example lo-

gistic loss or hinge loss. Let Y be a real-valued (response) variable andX be a (co-)variable

with values in some space X . Let

F ⊂ {fα =m

∑

k=1

αkψk}

be a (convex subset of a) linear space of functions on X . Here, {ψk}mk=1 is a given system

of base functions. Let γf : R × X → R be some loss function, and let {(Yi,Xi)}ni=1 be

i.i.d. copies of (X,Y ). We consider the estimator

f = arg minfα∈F

{

1

n

n∑

i=1

γf (Yi,Xi) + λI(α)

}

,

where I(α) :=∑m

k=1 τk|αk|denotes the weighted ℓ1 norm of the vector α ∈ Rm with

random weights τk := ( 1n

∑ni=1 ψ

2k(Xi))

1/2. We study the situation where the number of

parameters m is large (possibly much larger than the number of observations n). Our

purpose is threefold. Firstly, we want to show that for a proper choice of the smoothing

parameter λ ( possibly depending on {τk}), the estimator f satisfies an oracle inequality.

Secondly, we want the result to hold without any a priori bounds on the functions in F .

Thirdly, we aim at “reasonable” values for the constants involved, as indication that the

result is not merely an asymptotic one. In certain settings, the smoothing parameter λ can

be chosen asymptotically equal to 4√

2 logm/n, which is four times as large as in the linear

Gaussian case with soft thresholding. The factor 4 comes from using a symmetrization

and a contraction inequality.

27

Estimating Function Based Cross-validation

Mark van der Laan

Division of Biostatistics, University of California, Berkeley

Suppose that we observe a sample of independent and identically distributed realiza-

tions of a random variable. Given a model for the data generating distribution, assume

that the parameter of interest can be characterized as the parameter value which makes

the population mean of a possibly infinite dimensional estimating function equal to zero.

Given a collection of candidate estimators of this parameter, and specification of the vec-

tor estimating function, we propose a norm of the cross-validated estimating equation as

criteria for selecting among these estimators. For example, if we use the Euclidean norm,

then our criteria is defined as the Euclidean norm of the empirical mean over the validation

sample of the estimating function at the candidate estimator based on the training sam-

ple. We establish a finite sample inequality of this method relative to an oracle selector,

and illustrate it with some examples. This finite sample inequality provides us also with

asymptotic equivalence of the selector with the oracle selector under general conditions.

We also study the performance of this method in the case that the parameter of interest

itself is pathwise differentiable (and thus, in principle, root-n estimable).

An Expansion for A Discrete Non-lattice Distribution

Willem R. van Zwet

Department of Statistics, University of Leiden

Much is known about asymptotic expansions for asymptotically normal distributions

if these distributions are either absolutely continuous or pure lattice distributions. In this

paper we begin an investigation of the discrete but non-lattice case. We tackle one of the

simplest examples imaginable and find that curious phenomena occur. Clearly more work

is needed. (Co-author Friedrich Gotze)

Flexible Approaches to Model Survival and LongitudinalData Jointly

Jimin Ding and Jane-Ling Wang (Speaker)

Department of Statistics, University of California at Davis

In clinical studies, longitudinal covariates are often used to monitor the progression

of the disease as well as survival time. Relationship between a failure time process and

some longitudinal covariates is of key interest and so is the understanding of the pattern

28

of longitudinal process to learn more about health status of patients, or to get some

insight into the progression of disease. Joint modeling of the longitudinal and survival

data has certain advantages and emerged as an effective way to handle both types of data

simultaneously. In this talk, we will explore several intriguing and challenging issues in

joint modelling.

Typically, a parametric longitudinal model is assumed to facilitate the likelihood ap-

proach. However, the choice of a proper parametric model turns out more illusive than

standard longitudinal studies where no survival end-point occurs. Furthermore, the com-

putational burden due to both Monte Carlo numerical integration and EM (Expected

Maximum) algorithm is an important concern in the joint modelling setting. To deal with

those challenges, we propose several flexible longitudinal models in the joint modelling

setting. Simplicity of the model structure is crucial to have good numerical stability, and

we will illustrate this through numerical studies and data analysis.

Goodness of Fit via Phi-divergences: A New family of TestStatistics

Jon A. Wellner

Department of Statistics, University of Washington

A new family of goodness-of-fit tests based on phi-divergences is introduced and

studied. The new family is based on phi-divergences somewhat analogously to the phi-

divergence tests for multinomial distributions introduced by Cressie and Read (1984), and

is indexed by a real parameter s ∈ R: s = 2 gives the Anderson - Darling test statistic,

s = 1 gives the Berk-Jones test statistic, s = 1/2 gives a new (Hellinger - distance type)

statistic, s = 0 corresponds to the “reversed Berk-Jones” statistic, and s = −1 gives a

“studentized” (or empirically weighted) version of the Anderson - Darling statistic. We

also introduce corresponding integral versions of the new statistics.

We show that the asymptotic null distribution theory of Jaeschke (1979) and Eicker

(1979) for the Anderson-Darling statistic, and of Berk and Jones (1979) applies to the

whole family of statistics Sn(s) with s ∈ [−1, 2]. We also provide new finite-sample

approximations to the null distributions and show how the new approximations can be

used to obtain accurate computation of quantiles.

On the side of power behavior, we show that for 0 < s < 1 and fixed alternatives

the test statistics always converge almost surely to their corresponding natural parameter.

For 1 < s <∞ we provide necessary and sufficient conditions on the alternative d.f. F for

convergence to the corresponding natural parameter to hold, and show that the “Poisson

boundary” phenomena noted by Berk and Jones for their statistic continues to hold for

s ≥ 1 and s < 0 by identifying the Poisson boundary distributions explicitly.

29

We extend the results of Donoho and Jin (2004) by showing that all our new tests

for s ∈ [−1, 2] have the same “optimal detection boundary” for normal shift mixture

alternatives as Tukey’s “higher-criticism” statistic and the Berk-Jones statistic.

Heterogeneous Autoregressive Realized Volatility Model

Yazhen Wang

Department of Statistics, University of Connecticut

Volatilities of asset returns are pivotal for many issues in financial economics. The

availability of high frequency intraday data should allow us to estimate volatility more

accurately. Realized volatility is often used to estimate integrated volatility. To obtain

better volatility estimation and forecast, some autoregressive structure of realized volatility

is proposed in the literature. This talk will present my recent work on heterogeneous

autoregressive models of realized volatility.

Bayesian Hierarchical Modeling for IntegratingLow-accuracy and High-accuracy Experiments

Jeff Wu

Georgia Institute of Technology, School of Industrial and Systems Engineering

Standard practice in analyzing data from different types of experiments is to treat data

from each type separately. By borrowing strength across multiple sources, an integrated

analysis can produce better results. Careful adjustments need to be made to incorpo-

rate the systematic differences among various experiments. To this end, some Bayesian

hierarchical Gaussian process models (BHGP) are proposed. The heterogeneity among

different sources is accounted for by performing flexible location and scale adjustments.

The approach tends to produce prediction closer to that from the high-accuracy experi-

ment. The Bayesian computations are aided by the use of Markov chain Monte Carlo and

Sample Average Approximation algorithms. The proposed method is illustrated with two

examples: one with detailed and approximate finite elements simulations for mechanical

material design and the other with physical and computer experiments. (Based on joint

work with Zhiguang Qian).

30

Semiparametric Mixed Effects Models for Duration andLongitudinal Data

Zhiliang Ying

Department of Statistics, Columbia University

In this talk, I will present a doubly semiparametric mixed effects model for duration and

recurrent event time data. This model is useful in accommodating possible informative

censoring, a common problem in many follow-up studies. It also exhibits interesting

features which make it relatively easy to carry out the usual statistical inferences. We

show the usefulness and practicality of the proposed approach via theoretical properties,

simulation results and data analysis. Some additional developments on linear mixed effects

model for longitudinal data will also be presented.

Spatially Adaptive Functional Linear Regression withFunctional Smooth Lasso

Chunming Zhang

Department of Statistics, University of Wisconsin

In this paper we consider the setting where the regressor is a functional data such as a

curve or an image and the response is a scalar. We propose the “functional smooth lasso”

(FSL) approach to simultaneously regularize the roughness and the size of the nonzero

regions of the functional linear regression estimates. An efficient algorithm is developed

for computing FSL. The degrees of freedom of FSL is derived and incorporated into the

automatic tuning of regularization parameters. Furthermore, we prove the consistency and

the convergence rate of FSL. An interesting finding is that the convergence rate depends

on the degree of the ”smoothness” of the predictors. The proposed method is illustrated

via simulation studies and real data application.

Multi-Dimensional Trimming Based on Data Depth

Yijun Zuo

Department of Statistics and Probability, Michigan State University, East Lansing

With a natural order principle, trimming in one dimension is straightforward. One-

dimensional trimmed means are among the most popular estimators of the center of data

and have been used in various fields of statistics and in our daily life. Trimmed means

can overcome the high sensitivity of the mean to outliers (or heavy-tailed data) and the

low efficiency of the median for light-tailed data. Hence they can serve as compromises

between the mean and the median.

31

Multi-dimensional data often contain outliers, which typically are far more difficult to

detect than in one dimension. A robust procedure such as the multi-dimensional trimming

that can automatically detecting outliers or “heavy tails” is thus desirable. The task of

trimming, however, becomes non-trivial, for there is no natural order principle in high

dimensions. In this talk, multi-dimensional trimming based on “data depth” is discussed.

It is found that depth-trimmed means can possess very desirable properties such as high

efficiency and high robustness. Furthermore, inference procedures based on the depth-

trimmed means can outperform the classical Hotelling’s T 2 (and the univariate t) ones.

Applications of data depth trimming such as clustering and dimension reduction are also

addressed. Contributions of Professor Bickel to trimming are discussed.

32

Workshop Participants

Name Institution Email Address

Yacine Ait-Sahalia Princeton University yacine@Princeton.EDU

Beth Andrews Northwestern University bandrews@northwestern.edu

Donald W.K. Andrews Yale University donald.andrews@yale.edu

Alex Bajamonde Genentech Inc. bajamonde.alex@gene.com

Peter J. Bickel Univ. of California, Berkeley bickel@stat.berkeley.edu

Steinar Bjerve University of Oslo steinar@math.uio.no

David Blei Princeton University blei@cs.princeton.edu

Howard Bondell North Carolina State Univ. bondell@stat.ncsu.edu

Peter Buhlmann Swiss Federal Institute of Tech. Zurich peter.buehlmann@stat.math.ethz.ch

Christopher Calderon Princeton University ccaldero@princeton.edu

Melissa Carroll Princeton University mkc@princeton.edu

Serena Chan Cornell University ssc35@cornell.edu

Scott Chasalow Bristol-Myers Squibb scott.chasalow@bms.com

Aiyou Chen Bell Labs, Lucent Tech. aychen@research.bell-labs.com

Ming-Yen Cheng National Taiwan University cheng@math.ntu.edu.tw

Shojaeddin Chenouri University of Waterloo schenouri@uwaterloo.ca

Laura Chioda Princeton University lchioda@princeton.edu

Gregory Chow Princeton University gchow@Princeton.EDU

Erhan Cinlar Princeton University ecinlar@princeton.edu

Anirban Dasgupta Purdue University dasgupta@stat.purdue.edu

Savas Dayanik Princeton University sdayanik@princeton.edu

Aurore Delaigle Univ. of California, San Diego delaigle@math.ucsd.edu

Jimin Ding Univ. of California, Davis jmding@wald. ucdavis.edu

Kjell Doksum Univ. of California, Berkeley doksum@stat.wisc.edu

David Donoho Stanford University donoho@stanford.edu

Miriam G. Donoho San Jose State Univ. donoho@email.sjsu.edu

Juan Du Michigan State University dujuan@msu.edu

Veronica Esaulova Otto von Guericke Univ. veronica.esaulova@gmail.com

Yingying Fan Princeton University yingying@princeton.edu

Julian Faraway University of Michigan faraway@umich.edu

Luisa T. Fernholz Princeton University lfernhol@princeton.edu

Don Fraser University of Toronto dfraser@utstat.toronto.edu

Mendel Fygenson Univ. of Southern California fygenson@marshall.usc.edu

33

Workshop Participants

Name Institution Email Address

Anne Gadermann Univ. of British Columbia gaderman@interchange.ubc.ca

Ursula Gather University of Dortmund gather@statistik.uni-dortmund.de

Zhiyu Ge Merrill Lynch gary−ge@mil.com

Jayanta K. Ghosh Purdue University ghosh@stat.purdue.edu

Sujit Ghosh North Carolina State Univ. sghosh@stat.ncsu.edu

Subhashis Ghoshal North Carolina State Univ. ghosal@stat.ncsu.edu

Friedrich Goetze University of Bielefeld goetze@mathematik.uni-bielefeld.de

Wenceslao G. Manteiga Univ. of Santiago de Compostela wenceslao@usc.es

Jiezhun Gu North Carolina State Univ. jgu@unity.ncsu.edu

Arjun Gupta Bowling Green State Univ. gupta@bgnet.bgsu.edu

Peter G. Hall The Australian National Univ. Peter.Hall@maths.anu.edu.au

Hillary Han Cornell University hillary−han@yahoo.com

Jaroslaw Harezlak Harvard University jharezla@hsph.harvard.edu

Nick Hengartner Los Alamos National Laboratory nickh@lanl.gov

Moonseong Heo Cornell University moh2002@med.Cornell.edu

David Hitchcock Univ. of South Carolina hitchcock@stat.sc.edu

Haiyan Huang Univ. of California at Berkeley hhuang@stat.berkeley.edu

Li-Shan Huang University of Rochester Lhuang@bst.rochester.edu

Tao Huang Yale University t.huang@yale.edu

Ben Huang Bristol-Myers Squibb shupang.huang@bms.com

Xiaoming Huo Univ. of California at Riverside xmhuo@ucr.edu

Ed Ionides University of Michigan inides@umich.edu

Barry James Univ. of Minnesota, Duluth bjames@d.umn.edu

Kang James Univ. of Minnesota Duluth kjames@d.umn.edu

Yuan Ji The University of Texas yuanji@mdanderson.org

Jiancheng Jiang Princeton University jjiang@princeton.edu

Jiming Jiang University of California, Davis jiang@wald.ucdavis.edu

Kun Jin FDA/CDER/OB/DBI JINK@cder.fda.gov

Zhezhen Jin Columbia University zj7@columbia.edu

Rebecha Jornsten Rutgers University rebecka@stat.rutgers.edu

Noureddine El Karoui UC Berkeley nkaroui@stat.berkeley.edu

Katerina Kechris Univ. of Colorado Health Sci. Center katerina.kechris@uchsc.edu

Abbas Khalili University of Waterloo aa2mahmo@math.uwaterloo.ca

Chris Klaassen Universiteit van Amsterdam chrisk@science.uva.nl

Hira Koul Michigan State University koul@stt.msu.edu

34

Workshop Participants

Name Institution Email Address

Sanjeev Kulkarni Princeton University kulkarni@princeton.edu

Jaimyoung Kwon Cal State East Bay jaimyoung.kwon@csueastbay.edu

Soumendra N. Lahiri Iowa State University snlahiri@iastate.edu

Clifford Lam Princeton University wlam@princeton.edu

Hyunsook Lee Pennsylvania State Univ. hlee@stat.psu.edu

Elizaveta Levina University of Michigan elevina@umich.edu

Michael Levine Purdue University mlevins@stat.purdue.edu

Hongzhe Li University of Pennsylvania hli@cceb.upenn.edu

Lexin Li North Carolina State Univ. li@stat.ncsu.edu

Runze Li Pennsylvania State Univ. rli@stat.psu.edu

Chaobin Liu Bowie State University cliu@bowiestate.edu

Jun Liu Harvard University jliu@stat.harvard.edu

Mengling Liu New York University mengling.liu@med.nyu.edu

Regina Liu Rutgers University rliu@stat.rutgers.edu

Yanning Liu Cornell University yl229@cornell.edu

Yufeng Liu Univ. of North Carolina yfliu@email.unc.edu

Markus Loecher Rutgers University loecher@mailaps.org

Adriana Lopes University of Pittsburgh ad15@pitt.edu

Panos Lorentziadis Hellenic American Univ. paloren@attglobal.net

Aurelie Lozano Princeton University alozano@princeton.edu

Ying Lu Harvard University ylu@latte.harvard.edu

Jun Luo Michigan State University luojun@msu.edu

Jinchi Lv Princeton University jlv@princeton.edu

Loriano Mancini University of Zrich mancini@isb.unizh.ch

David Masson University of Delaware davidm@udel.edu

Jon McAuliffe University of Pennsylvania mcjon@wharton.upenn.edu

Anjana Meel University of Pennsylvania anjanam@seas.upenn.edu

Xiaoli Meng Harvard University meng@stat.harvard.edu

Oksana Mokliatchouk Bristol-Myers Squibb oksana.mokliatchouk@bms.com

Stephan Morgenthaler EPFL Learning Center stephan.morgenthaler@epfl.ch

Akira Morita Georgia Tech gtg347v@mail.gatech.edu

Hans Mueller Univ. of California Davis mueller@wald.ucdavis.edu

Yolanda Munoz University of Texas Yolanda.M.Munoz@uth.tmc.edu

Vijay Nair University of Michigan vnn@umich.edu

Jan Neumann Simens Corporate Research jan.neumann@siemens.com

Yue Niu Princeton University yniu@princeton.edu

35

Workshop Participants

Name Institution Email Address

Juan Carlos Pardo University of Vigo juancp@uvigo.es

Byeong Park Seoul National University bupark@stats.snu.ac.kr

Emanuel Parzen Texas A&M University eparzen@stat.tamu.edu

Heng Peng Princeton University pheng@princeton.edu

Jianan Peng Acadia University jianan.peng@acadiau.ca

Quang Pham University of Alaska Fairbanks pxquang@cox.net

Nancy Reid University of Toronto reid@utstat.edu

Philip Reiss Columbia University ptr2003@columbia.edu

John Rice Univ. of California, Berkeley rice@stat.Berkeley.EDU

Yaacov Ritov Israel Social Sci. Data Center yaacov.ritov@huji.ac.il

Alex Rojas Carnegie Mellon University arojas@stat.cmu.edu

Juan Romo Universidad Carlos III de Madrid juan.romo@uc3m.es

Kaisiromwe Sam Uganda Bureau of Statistics sam.kaisiromwe@ubos.org

Alexander Samarov MIT samarov@mit.edu

Richard Samworth University of Cambridge rjs57@cam.ac.uk

Stanley Sawyer Washington University sawyer@math.wustl.edu

Robert Schapire Princeton University schapire@cs.princeton.edu

Anton Schick Binghamton University anton@math.binghamton.edu

Damla Senturk Penn State Univ. dsenturk@stat.psu.edu

Chris Sims Princeton University sims@princeton.edu

Dan Spitzner Virginia Tech dan.spitzner@vt.edu

Curtis Storlie North Carolina State Univ. storlie@stat.ncsu.edu

Umar Syed Princeton University usyed@cs.princeton.edu

Nian-Sheng Tang Columbia University nstang@ynu.edu.cn

Shijie Tang Univ. of Wisconsin at Madison tangs@stat.wisc.edu

Tiejun Tong Yale University tiejun.tong@yale.edu

David Tyler Rutgers University dtyler@rci.rutgers.edu

Sara van der Geer Swiss Federal Institute of Tech. Zurich geer@math.leidenuniv.nl

Mark van der Laan Univ. of California, Berkeley laan@stat.Berkeley.EDU

Willem van Zwet University of Leiden vanzwet@math.leidenuniv.nl

Bob Vanderbei Princeton University rvdb@princeton.edu

Aldo Jose Viollaz Univ. Nac. De Tucuman aviollaz@herrera.unt.edu.ar

Haiyan Wang Kansas State University hwang@ksu.edu

Jane-Ling Wang Univ. of California at Davis wang@wald.ucdavis.edu

Naisyin Wang Texas A&M University nwangstat@gmail.com

Paul C. Wang CPR & CDR Technologies, Inc pcwang@cprcdr.com

36

Workshop Participants

Name Institution Email Address

Qing Wang Princeton University qingwang@princeton.edu

Xiaohui Wang University of Virginia xw5a@virginia.edu

Yonghua Wang Bristol-Myers Squibb yonghua.wang@bms.com

Jon Wellner University of Washington jaw@stat.washington.edu

Roy Welsch MIT rwelsch@mit.edu

Yazhen Wang University of Connecticut yzwang@stat.uconn.edu

Baolin Wu University of Minnesota baolin@biostat.umn.edu

Jeff C. Wu Georgia Institute of Tech. jeffwu@isye.gatech.edu

Qiang Wu University Pittsburgh qiw8@pitt.edu

Yichao Wu University of North Carolina wuy@email.unc.edu

Joseph A. Yahav The Hebrew Univ. of Jerusalem j-ya@bezeqint.net

Zhiliang Ying Columbia University zying@stat.columbia.edu

Angela Yu Princeton University ajyu@princeton.edu

Peng Zeng Auburn University zengpen@auburn.edu

Chongqi Zhang Guangzhou University chongqi@gzhu.edu.cn

Chunming Zhang Univ. of Wisconsin at Madison cmzhang@stat.wisc.edu

Hao Zhang North Carolina State Univ. hzhang@stat.ncsu.edu

Heping Zhang Yale University heping.zhang@yale.edu

Jingjin Zhang Princeton University jingjinz@princeton.edu

Jin-Ting Zhang National Univ. of Singapore stazjt@nus.edu.sg

Zhengjun Zhang Univ. of Wisconsin at Madison zjz@stat.wisc.edu

Zhigang Zhang Oklahoma State Univ. zhigang.zhang@okstate.edu

Tian Zheng Columbia University tzheng@stat.columbia.edu

Jianhui Zhou University of Virginia jz9p@virginia.edu

Hongtu Zhu Columbia University hz2114@columbia.edu

Ji Zhu University of Michigan jizhu@umich.edu

Hui Zou University of Minnesota hzou@stat.umn.edu

Yijun Zuo Michigan State University zuo@stt.msu.edu

37

Frontiers of Statistics

— in honor of Professor Peter J. Bickel’s 65th Birthday

Edited by Jianqing Fan and Hira L. Koul

Imperial College Press

Table of Contents

1. Our Steps on the Bickel WayKjell Doksum and Ya’acov Ritov 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Doing Well at a Point and Beyond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Robustness, Transformations, Oracle-free Inference, and Stable Parameters . . . . . . . . 4

1.4 Distribution Free Tests, Higher Order Expansions, and Challenging Projects . . . . . . . 4

1.5 From Adaptive Estimation to Semiparametric Models . . . . . . . . . . . . . . . . . . . . 5

1.6 Hidden Markov Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.7 Non- and Semi-parametric Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.8 The Road to Real Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Bickel’s Publication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Part I. Semiparametric Modeling

2. Semiparametric Models: A Review of Progress since BKRW (1993)Jon A. Wellner, Chris A. J. Klaassen and Ya’acov Ritov 25

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.2 Missing Data Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.3 Testing and Profile Likelihood Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.4 Semiparametric Mixture Model Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.5 Rates of Convergence via Empirical Process Methods . . . . . . . . . . . . . . . . . . . . 30

2.6 Bayes Methods and Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.7 Model Selection Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.8 Empirical Likelihood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.9 Transformation and Frailty Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.10 Semiparametric Regression Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.11 Extensions to Non-i.i.d. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.12 Critiques and Possible Alternative Theories . . . . . . . . . . . . . . . . . . . . . . . . . 35

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3. Efficient Estimator for Time SeriesAnton Schick and Wolfgang Wefelmeyer 45

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.2 Characterization of Efficient Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.3 Autoregression Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.4 Innovation Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.5 Innovation Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.6 Conditional Expectation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.7 Stationary Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.8 Stationary Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.9 Transition Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

38

4. On the Efficiency of Estimation for a Single-index ModelYingcun Xia and Howell Tong 63

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.2 Estimation via Outer Product of Gradients . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.3 Global Minimization Estimation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.4 Sliced Inverse Regression Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.5 Asymptotic Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.6 Comparisons in Some Special Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.7 Proofs of the Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5. Estimating Function Based Cross-ValidationM.J. van der Laan and Dan Rubin 87

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.2 Estimating Function Based Cross-Validation . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.3 Some Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

5.4 General Finite Sample Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.5 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Part II. Nonparametric Methods

6. Powerful Choices: Tuning Parameter Selection Based on PowerKjell Doksum and Chad Schafer 113

6.1 Introduction: Local Testing and Asymptotic Power . . . . . . . . . . . . . . . . . . . . . 114

6.2 Maximizing Asymptotic Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

6.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

6.4 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

7. Nonparametric Assessment of AtypicalityPeter Hall and Jim W. Kay 143

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

7.2 Estimating Atypicality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

7.3 Theoretical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

7.4 Numerical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

7.5 Outline of Proof of Theorem 7.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

8. Selective Review on Wavelets in StatisticsYazhen Wang 163

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

8.2 Wavelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

8.3 Nonparametric Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

8.4 Inverse Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

8.5 Change-points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

8.6 Local Self-similarity and Non-stationary Stochastic Process . . . . . . . . . . . . . . . . 176

8.7 Beyond Wavelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

9. Model Diagnostics via Martingale Transforms: A Brief ReviewHira L. Koul 183

9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

9.2 Lack-of-fit Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

9.3 Censoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

9.4 Khamaladze Transform or Bootstrap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

39

Part III. Statistical Learning and Bootstrap

10. Boosting Algorithms: with an Application to Bootstrapping Multivariate TimeSeriesPeter Buhlmann and Roman W. Lutz 209

10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

10.2 Boosting and Functional Gradient Descent . . . . . . . . . . . . . . . . . . . . . . . . . . 211

10.3 L2-Boosting for High-dimensional Multivariate Regression . . . . . . . . . . . . . . . . . 217

10.4 L2-Boosting for Multivariate Linear Time Series . . . . . . . . . . . . . . . . . . . . . . . 222

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

11. Bootstrap Methods: A ReviewS. N. Lahiri 231

11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

11.2 Bootstrap for i.i.d Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

11.3 Model Based Bootstrap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

11.4 Block Bootstrap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

11.5 Sieve Bootstrap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

11.6 Transformation Based Bootstrap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244

11.7 Bootstrap for Markov Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

11.8 Bootstrap under Long Range Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . 246

11.9 Bootstrap for Spatial Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

12. An Expansion for a Discrete Non-Lattice DistributionFriedrich Gotze and Willem R. van Zwet 257

12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

12.2 Proof of Theorem 12.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262

12.3 Evaluation of the Oscillatory Term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

Part IV. Longtitudinal Data Analysis

13. An Overview on Nonparametric and Semiparametric Techniques for LongitudinalDataJianqing Fan and Runze Li 277

13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

13.2 Nonparametric Model with a Single Covariate . . . . . . . . . . . . . . . . . . . . . . . . 279

13.3 Partially Linear Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

13.4 Varying-Coefficient Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

13.5 An Illustration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

13.6 Generalizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294

13.7 Estimation of Covariance Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

14. Regressing Longitudinal Response Trajectories on a CovariateHans-Georg Muller and Fang Yao 305

14.1 Introduction and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

14.2 The Functional Approach to Longitudinal Responses . . . . . . . . . . . . . . . . . . . . 311

14.3 Predicting Longitudinal Trajectories from a Covariate . . . . . . . . . . . . . . . . . . . . 313

14.4 Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

40

Part V. Statistics in Science and Technology

15. Statistical Physics and Statistical Computing: A Critical LinkJames D. Servidea and Xiao-Li Meng 327

15.1 MCMC Revolution and Cross-Fertilization . . . . . . . . . . . . . . . . . . . . . . . . . . 328

15.2 The Ising Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

15.3 The Swendsen-Wang Algorithm and Criticality . . . . . . . . . . . . . . . . . . . . . . . 329

15.4 Instantaneous Hellinger Distance and Heat Capacity . . . . . . . . . . . . . . . . . . . . 331

15.5 A Brief Overview of Perfect Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334

15.6 Huber’s Bounding Chain Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336

15.7 Approximating Criticality via Coupling Time . . . . . . . . . . . . . . . . . . . . . . . . 340

15.8 A Speculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

16. Network Tomography: A Review and Recent DevelomentsEarl Lawrence, George Michailidis, Vijayan N. Nair and Bowei Xi 345

16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346

16.2 Passive Tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348

16.3 Active Tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352

16.4 An Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

16.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364

Part VI. Financial Econometrics

17. Likelihood Inference for Diffusions: A SurveyYacine Aıt-Sahalia 369

17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369

17.2 The Univariate Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371

17.3 Multivariate Likelihood Expansions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378

17.4 Connection to Saddlepoint Approximations . . . . . . . . . . . . . . . . . . . . . . . . . 383

17.5 An Example with Nonlinear Drift and Diffusion Specifications . . . . . . . . . . . . . . . 386

17.6 An Example with Stochastic Volatility . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

17.7 Inference When the State is Partially Observed . . . . . . . . . . . . . . . . . . . . . . . 391

17.8 Application to Specification Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399

17.9 Derivative Pricing Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400

17.10 Likelihood Inference for Diffusions under Nonstationarity . . . . . . . . . . . . . . . . . 400

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402

18. Nonparametric Estimation of Production EfficiencyByeong U. Park, Seok-Oh Jeong, and Young Kyung Lee 407

18.1 The Frontier Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407

18.2 Envelope Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409

18.3 Order-m Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417

18.4 Conditional Frontier Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421

18.5 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424

Part VII. Parametric Techniques and Inferences

41

19. Convergence and Consistency of Newton’s Algorithm for Estimating Mixing Dis-tributionJayanta K. Ghosh and Surya T. Tokdar 429

19.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429

19.2 Newton’s Estimate of Mixing Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . 431

19.3 Review of Newton’s Result on Convergence . . . . . . . . . . . . . . . . . . . . . . . . . 432

19.4 Convergence Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

19.5 Other Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438

19.6 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442

20. Mixed Models: An OverviewJiming Jiang and Zhiyu Ge 445

20.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445

20.2 Linear Mixed Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446

20.3 Generalized Linear Mixed Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450

20.4 Nonlinear Mixed Effects Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460

21. Robust Location and Scatter Estimators in Multivariate AnalysisYijun Zuo 467

21.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467

21.2 Robustness Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469

21.3 Robust Multivariate Location and Scatter Estimators . . . . . . . . . . . . . . . . . . . 473

21.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481

21.5 Conclusions and Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485

22. Estimation of the Loss of an EstimateWing Hung Wong 491

22.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491

22.2 Kullback-Leibler Loss and Exponential Families . . . . . . . . . . . . . . . . . . . . . . . 493

22.3 Mean Square Error Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495

22.4 Location Families . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496

22.5 Approximate Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498

22.6 Convergence of the Loss Estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506

Subject Index 507

Author Index 511

42

fÑxv|tÄ g{tÇ~á

go

Mary Beth Falke

Connie Brown

Zoya Kramer

and

Michael Bino, Lisa Glass, Noelina Hall , Kimberly Lupinacci

43