shanti swarup gupta (1925–2002): a tribute
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Shanti Swarup Gupta(1925–2002): A TributeS. Panchapakesana
a Department of Mathematics, Southern IllinoisUniversity, Carbondale, Illinois 62901Published online: 06 Aug 2013.
To cite this article: S. Panchapakesan (2009) Shanti Swarup Gupta (1925–2002):A Tribute, American Journal of Mathematical and Management Sciences, 29:1-2,15-24, DOI: 10.1080/01966324.2009.10737746
To link to this article: http://dx.doi.org/10.1080/01966324.2009.10737746
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AMERICAN JOURNAL OF MATHEMATICAL AND MANAGEMENT SCIENCES
Copyright© 2009 by American Sciences Press, Inc.
SHANTI SWARUP GUPTA (1925-2002): A TRIBUTE
S. Panchapakesan, Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901
Shanti S. Gupta was a pioneer in the field of Selection and Ranking. His
phenomenal contributions to this area not only span various aspects of the
problem but also continue to have significant impact and influence on the
developments in those directions. Over a period of 45 years, he authored or
coauthored two research level books, and 189 research papers published in
journals and special volumes. He also organized and co-edited the proceedings of
the first five Purdue Symposia on Statistical Decision Theory and Related Topics.
Key Words and Phrases: Shanti Gupta; biographical; professional
accomplishments; tribute
2009, VOL. 29, NOS. I & 2, 14-24 0196-6324/09/010014-11 $16.00
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16 S. PANCHAPAKESAN
Shanti earned his B.A. Honours and M.A. degrees, both in mathematics
from Delhi University in 1946 and 1949, respectively. Soon after his graduation
in 1949, he joined Delhi College, Delhi as a Lecturer in Mathematics and spent
the next four years teaching in the college. His early desire was to do Ph.D. at the
Delhi University in the area of astrophysics under the guidance of Professor P. L.
Bhatnagar. His initial pursuit in this direction did not go very far because
Bhatnagar got an invitation to go to Harvard University's astronomical center for
a year or two. At this juncture, Shanti became interested in learning probability
and statistics. While still teaching at Delhi College, he joined the one-year
diploma course in applied statistics conducted by the Indian Council of
Agricultural Research {ICAR). At ICAR, he attended courses taught by several
prominent Indian statisticians, including Raghu Raj Bahadur and Pandurang V.
Sukatme.
By the time Shanti completed the ICAR diploma course, his interest in
statistics got deeper. In the Spring of 1953, he received a Fulbright travel grant
plus a Smith-Mundt Scholarship for one year graduate study in the United States.
Although he had a few universities in mind as possible places to attend, the
Fulbright Scholarship Committee had already arranged for him to be placed at the
University of North Carolina, one of the flourishing places for statistics at that
time. Shanti continued as a graduate student at Chapel Hill from 1953 to 1956 and
wrote his Ph.D. thesis ( 1956) under the guidance of Professor Raj Chandra Bose.
In his thesis entitled On A Decision Rule for A Problem in Ranking Means , Shanti
investigated the problem of selecting the normal population having the largest
mean (target population) from several normal populations that have a common
known or unknown variance. The goal is to select a non-empty subset of the given
populations so that the probability of not including the target population in the
selected subset is at most a (pre-specified). This means that the probability of
including the target population in the selected subset is at least 1- a ; this was
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SHANT! S. GUPTA: A TRIBUTE 17
called by him the coefficient of safety and came to be known later as the
guaranteed probability of a correct selection and usually denoted by P *. In the
case of unknown common variance, he derived his decision rule by pairwise
application of the 3-decision rule of Bahadur ( 1952) based on the /-statistic for
ranking means of two normal populations. In the special case of common known
variance and a slippage configuration for the unknown means, he showed that his
rule followed from the likelihood ratio test or from the union-intersection
principle of Roy (1953). Earlier, K. C. Seal in his 1954 Ph.D. thesis under R. C.
Bose considered a general class of decision rules for ranking normal means and
showed that one particular member of this class, to be known later as the average
type rule, has some optimal properties. These results are discussed in Seal (1955).
Shanti Gupta's rule is also a member of Seal's general class and came to be
known as the maximum-type rule. Shanti, in his thesis, showed that his
maximum-type rule performed better than the average-type rule in many
situations. This fact, combined with the mathematical tractability of his rule was
central to the rich growth of the subset selection theory.
Several publications came out over the years based on the investigations in
Shanti's thesis. Implementation of his subset selection rule involves evaluation of
appropriate constant as a percentage point of the distribution of
Y=(X1p1 -X0 )fsv, where X1p1 =max(X,, . .. ,Xp) with all the p+1 variables
independently and identically distributed N(O,a 2) and s,: (distributed as
a 2 x: /v) is an estimator of a 2 independent of all the X;. Gupta and Sobel
(1957) have discussed several different methods of computing the probability
integral and percentage points of Y. In his thesis, Shanti Gupta also showed that
the probability integral of Y can be obtained as the solution of a difference
differential equation discussed by Hartley (1943-46). Using this method, Gupta,
Panchapakesan and Sohn ( 1985) tabulated the percentage points of the
Studentized maximum of equally correlated normal random variables. In the case
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18 S. PANCHAPAKESAN
ofknowncr, Shanti obtained in his thesis the moments of U=(X1P1-X0 )/cr
through an associated system of differential equations. Using this technique, Bose
and Gupta (1959) obtained the moments of X1,l' rth order statistic from a
sample of size n from a standard normal distribution. Incidentally, this happens to
be the only joint paper by Shanti Gupta and R. C. Bose. Gupta (1963) tabulated
the probability integral of the maximum of equally positively correlated standard
normal variables and its percentage points in the case of equal correlation being
0.5; these are the percentage points of U needed to implement his subset selection
rule in the case of common known variance. Later, Gupta, Nagel and
Panchapakesan (1973) tabulated the percentage points for various selected values
of the positive equal correlation. These tables are useful in many contexts,
especially in ranking and selection, and are widely referenced in the literature.
Robert Bechhofer, Shanti Gupta and Milton Sobel are the three acclaimed
pioneers of the field of Ranking and Selection. It is perhaps interesting to note
that of the three Shanti Gupta was the only one who started his career by writing a
Ph.D. thesis in the area. Bechhofer got his Ph.D. in 1951 from Columbia
University under the guidance ofT. W. Anderson. In the academic year 1952-53,
he accepted a Research Associate position at Cornell University. During this time,
his friend Cuthbert Daniel asked him how to calculate the probability that for
normal populations the sample means will line up in the same way as the
population means. His attempt to find the answer to this question, led Bechhofer
to his selection and ranking formulation (see Bechhofer, 1985). After receiving
his Ph.D. from Columbia in 1951, Milton Sobel joined as Research Associate at
Cornell. This set the stage for the collaboration between Bechhofer and Sobel. In
1954, Milton joined Bell Telephone Laboratories in Allentown, Pennsylvania, as
a Research Statistician with the Statistics and Reliability Group. Shanti Gupta
joined the Laboratories in 1956. During their stay in the Laboratories, Shanti and
Milton had a very active and fruitful collaboration.
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SHANT! S. GUPTA: A TRIBUTE 19
Shanti Gupta's research career was mostly devoted to ranking and selection
problems; he became the leading advocate for the subset selection approach. His
contributions to this area relate to various aspects and cover a wide range of topics
such as specific univariate distributions, multinomial and multivariate normal
populations, restricted families of distributions like IFR and IFRA families,
isotonic procedures, decision-theoretic formulations, Bayes and empirical Bayes
procedures, and estimation after selection.
Shanti 's interest in order statistics went deeper than the usual connection
with ranking and selection procedures. His contributions in the area of order
statistics cover distribution theory, computation of moments and quantiles, and
estimation theory. During his years at the Bell Telephone Laboratories, he
developed his interest in reliability theory. His contributions in this area include
not only selection procedures related to reliability models but also sampling plans
based on life tests for the gamma, normal and log-normal distributions and for
IFR family. His contributions also include estimation based on Type-II censored
samples and life testing for multi-component systems.
Shanti Gupta held his position at Bell Telephone Laboratories in
Allentown until the Autumn of 1961 except for the academic year 1957-58 when
he was Associate Professor at The University of Alberta, Canada. Before starting
his year at Alberta, he had a summer appointment at Northern Electric in
Montreal. During 1959-61 , while serving at Bell Laboratories, he taught evening
classes at the Courant Institute of Mathematical Sciences as an Adjunct Associate
Professor. In 1961, he decided to embark on a full-time academic career. During
1961-62, he held a visiting position as Associate Professor at Stanford University
and in the Fall of 1962 he joined the Division of Mathematical Sciences at Purdue
University as a Professor of Mathematics and Statistics. In 1965, he became the
Head of the newly started Department of Statistics at Purdue. He remained Head
until 1995 when he decided to step down and continued to teach until his death in
January 2002. Under his leadership, the department became one of the foremost
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20 S. PANCHAPAKESAN
centers of research and training in statistics. His grand success as the head of the
department was evident from the fact that his colleagues in the department or the
administrators never thought of a successor until he decided to step down!
Besides meeting the demands of the day-to-day administration of the
department and teaching his seminar course, Shanti guided in all 30 Ph.D.
dissertations at Purdue, with the last student finishing in 2001. It was remarkable
that he never voluntarily lost touch with any of his students. He founded the
Purdue International Symposium Series on Statistical Decision Theory and
Related Topics and personally organized the first five that took place before his
death. In 1988, he established a Center for Statistical Decision Sciences at Purdue
and served as a Co-Director until his death. Purdue University, in recognition of
his services to the university and the statistical profession at large, created in 1996
the Shanti S. Gupta Distinguished Professorship for excellence in teaching.
Shanti Gupta rendered distinguished service to the statistical community at
large in various ways and capacities. These included high-level committee
assignments in professional societies and editorial assignments for several
journals. We mention here two important ones: President of the Institute of
Mathematical Statistics (1989-90) and Editor-in-Chief of Journal of Statistical
Planning and Inference (1989-91). He received several honors. He was a Fellow
of the American Statistical Association, the American Association for the
Advancement of Sciences, and the Institute of Mathematical Statistics. He was an
elected member of the International Statistical Institute. Some special short-term
visiting positions held by him include Special Chair, Institute of Mathematics,
Academia Sinica, Taipei, Taiwan; Erskine Fellow, University of Canterbury,
Christ Church, New Zealand; and Guest Professor, Institute of Mathematics,
Technical University, Darmstadt, Germany. He was one of the Special Invitees at
the 1995 Taipei International Symposium in Statistics. On that occasion, he was
presented with the key to the city by the Mayor of Taipei; this is something he
would always recall with relish!
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SHANT! S. GUPTA: A TRIBUTE 21
1 have given here only brief account of the extent of his contributions to
the field of Ranking and Selection and to the statistical profession in general. A
biographical article by Panchapakesan and Santner ( 1985) discusses his research
contributions in a special volume of American Journal of Mathematical and
Management Sciences dedicated to him, Bechhofer and Sobel for their pioneering
contributions to the field of Ranking and Selection The volume was brought out
to mark three decades of developments in the field. Gupta and Panchapakesan
(1985) in their article in this special volume have reviewed the developments in
the subset selection theory to date since the beginning. As one can surmise, this is
also substantially the contributions made by Shanti Gupta and his students. An
update of the article by Panchapakesan and Santner ( 1985) is provided by Santner
and Panchapakesan (2002) which updates Shanti's list of publications and
includes a chronological list of his Ph.D. students with their current employment
status. "A Conversation with Shanti Gupta" by Gary McDonald (1998) in
Statistical Science conversation series provides an account of his early education,
graduate student days at Chapel Hill, professional associates and
accomplishments, and his views on contemporary statistical developments. In
1997, a special volume edited by S. Panchapakesan and N Balakrishnan,
Advances in Statistical Decision Theory and Applications (Birkhauser), was
published in Shanti's honor. This volume contains 28 research articles by his
colleagues, associates and former students. Besides his list of publications to date,
the book also gives a chronological list of his Ph.D. students with their
dissertation titles and years. Two more articles dealing with Shanti's life and
accomplishments are the encyclopedia article by Panchapakesan (2006a) and the
article by Panchapakesan (2006b), giving a complete list ofShanti's publications,
that appeared in a special issue of the Journal of Statistical Planning and
Inference brought out in Shanti's memory.
My personal interaction with Shanti Gupta started in the Fall of 1965
when I came to Purdue to do my Ph.D. in statistics. When I went to see him in his
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22 S. PANCHAPAKESAN
office, he said that I could sign up for the two-semester seminar course he was
teaching. I took the course, rather unusually, in my first year. In the class, he
would discuss important research papers published in the journals. He would also
discuss papers dealing with estimation and moments from the book edited by
Sarhan and Greenberg (1962). He would explain the main ideas of a paper and
very soon would pose research questions to the students. His research seminar
varied in content from year to year as the literature on Ranking and Selection
grew. At the end of Summer of 1966, he offered me a Research Assistantship on
his Air Force research contract. Thus started my research collaboration with him.
When the time came to find a thesis advisor it became a foregone conclusion that
he will be my advisor. In 1968, we embarked on a project of preparing a survey
monograph on ranking and selection discussing significant results along with a
comprehensive bibliography. We wanted the monograph to serve as a reference
source for users and also be useful in delineating directions for future research.
This effort continued, keeping up with the increased pace of research in the area,
until we came to the point that it was essential to have the material available to the
researchers and practitioners. The result was our book Multiple Decision
Procedures: Theory and Methodology of Selecting and Ranking Population
published in 1979 by John Wiley and Sons. When we started the project in 1968,
there were less than hundred papers directly devoted to ranking and selection. The
bibliography in our book contains 600 plus entries. This book was republished in
2002 by SIAM in their Classics Series in Applied Mathematics. Unfortunately,
Shanti was not alive to see the realization of his efforts in this respect.
My personal and professional association with Shanti Gupta continued
after my Ph.D. in 1969 and endured till his last day.
REFERENCES
Bahadur, R. R. (1952). A property of the !-statistic. Sankhya , 12, 79-88.
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SHANTI S. GUPTA: A TRIBUTE 23
Bechhofer, R. E. (1985). Selection and ranking procedures-some personal
reminiscences, and thoughts about its past, present, and future. American
Journal of Mathematical and Management Sciences, 5, 201-234.
Bose, R. C. and Gupta, S. S. (1959). Moments of order statistics from a normal
population. Biometrika, 46, 433-440.
Gupta, S. S. (1957). On a statistic which arises in selection and ranking problems.
Annals of Mathematical Statistics, 28,957-967.
Gupta, S. S. (1963). Probability integrals of multivariate normal and multivariate
I. Annals of Mathematical Statistics, 34, 792-828.
Gupta, S. S., Nagel, K. and Panchapakesan, S. (1973). On the order statistics from
equally correlated normal random variables. Biometrika, 60, 403-413.
Gupta, S. S. and Panchapakesan, S. (1985). Subset selection procedures: review
and assessment. American Journal of Mathematical and Management
Sciences, 5, 235-311.
Gupta, S. S., Panchapakesan, S. and Sohn, J. K. (1985). On the distribution of the
studentized maximum of equally correlated normal random variables.
Communications in Statistics - Simulation and Computation, 14, 103-135.
Hartley, H. 0. (1943-46). Studentization or the elimination of the standard
deviation of the parent population from the random sample distribution of
statistics. Biometrika, 33, 173-180.
McDonald, G. C. (1998). A conversation with Shanti Gupta. Statistical Science,
13, 291-305.
Panchapakesan, S. (2006a). Gupta, Shanti Swarup. In: Encyclopedia of Statistical
Sciences, Second Edition (Eds. N. Balakrishnan, C. Read and B.
Vidakovic), New York: John Wiley, Volume 5, pp. 3037-3039.
Panchapakesan, S. (2006b). Shanti Swarup Gupta: His life (1925-2002) and work.
Journal of Statistical Planning and Inference, 136, 1986-1998.
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Panchapakesan, S. and Santner, T. J. (1985). Shanti S. Gupta: an appreciation.
American Journal of Mathematical and Management Sciences, 5, 347-
369.
Roy, S. N. (1953). On a heuristic method of test construction and its use in
multivariate analysis. Annals of Mathematical Statistics, 24, 220-238.
Santner, T. J. and Panchapakesan, S. (2002). Professor Shanti Swamp Gupta.
American Journal of Mathematical and Management Sciences, 22, 173-
198.
Sarhan, A. E. and Greenberg, B. G. (1962). Contributions to Order Statistics .
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Seal, K. C. (1955). On a class of decision procedures for ranking means. Annals
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