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DESCRIPTIONCharles University. Founded 1348. Austria, Linz 16. – 18. 6. . 2003. Johann Kepler University of Linz. Johann Kepler University of Linz. AN ANALYSIS OF. AN ANALYSIS OF. THE CZECH ECONOMY. THE CZECH ECONOMY. IN TRANSITION. IN TRANSITION. Jan Ámos Víšek. Jan Ámos Víšek. FSV UK. - PowerPoint PPT Presentation
Founded 1348Charles University
Johann Kepler University of LinzJohann Kepler University of Linz
THE CZECH ECONOMYTHE CZECH ECONOMYFSV UKSTAKAN III STAKAN III Institute of Economic Studies Faculty of Social SciencesCharles UniversityPrague Institute of Economic Studies Faculty of Social SciencesCharles UniversityPrague
Jan mos VekJan mos VekIN TRANSITIONIN TRANSITIONAN ANALYSIS OFAN ANALYSIS OF Austria, Linz 16. 18. 6.. 2003
Schedule of today talk definiton, properties and how to apply The least trimmed squaresdefinition The least weighted squaresThey utilized -regression Galileo Galilie (1632) Roger Joseph Bocovich (1757) Pierre Simon Laplace (1793)(already Francis Ysidro Edgeworth ., 1887) A motivation for robust regression
(continued) Schedule of today talk separating market oriented part from the restLooking for the sense of division dividing the industries into two groups - whyAnalyzing the export from and FDI into the Czech republic 1994 separating market oriented parts from the rest for each year Analyzing the export from the Czech republic - 1993-1999
Why robust methods in regression ?What about to consider a minimal elipsoid containing a priori given number of observations.
So the solution seems to be simple !continuedWhy robust methods in regression ?
continuedWhy robust methods in regression ?(otherwise we lose some useful information) I am sorry but we have to invent a more intricate solution.
So, for the OLS we have the breakdown point equal zero (asymptotically) ! Minimal number of observations which can cause that estimator breaks down. Recalling that is breakdown point
Francis Ysidro Edgeworth, 1887 The method of the least squares is seen to be our best course when we have thrown overboard a certain portion of our data - a sort of sacrifice which has often to be made by those who sail the stormy seas of Probability.
One of really applicable 50% breakdown point estimator The Least Trimmed Squares - Rousseeuw (1983) . and that the order statistics are given by
Let us recall that for any the residuals are given as The optimal . . Then for any
Continued The Least Trimmed Squares- evidently 50% breakdown point - scale- and regression-equivariant - -consistent and asymptotically normal - nowadays easy to evaluate Advantages - high subsample sensitivity, i.e. can be (arbitrarily) high Disadvantage Rousseeuw, Leroy (1987) PROGRESS First proposal based on LMS, in fact, the trimmed least squares. Probably still in S-PLUS, e.g.. It did not work satisfactorily, sometimes very bad.
How to select h reasonably?Number of points of this cloud is . is only a bit smaller than
Algorithm for the case when n is large is described in:
Vek, J.. (1996): On high breakdown point estimation. Computational Statistics (1996) 11, 137 146.Vek, J.. (2000): On the diversity of estimates Computational Statistics and Data Analysis, 34, (2000), 67 89.ek, P., J. . Vek (2000): Least trimmed squares. XPLORE, Application guide, 49 64. One implementation is available in package XPLORE (supplied by Humboldt University), TURBO-PASCAL-version from me, MATLAB version from my PhD-student Libora Maek.
High subsample sensitivity, i.e. Disadvantage of LTS can be rather large (without control by design of experiment) Vek, J.. (1999): The least trimmed squares - random carriers. Bulletin of the Czech Econometric Society, 10/1999, 1 - 30. Vek, J.. (1996): Sensitivity analysis of M-estimates. Annals of the Instit. of Statist. Math. 48 (1996), 469 495. Sensitivity analysis of M-estimates of nonlinear regression model: Influence of data subsets. Annals of the Institute of Statistical Mathematics, 261 - 290, 2002. See also
Vek, J.. (2002): The least weighted squares I. The asymptotic linearity of normal equations. Bulletin of the Czech Econometric Society, no.15, 31 - 58, 2002. The least weighted squares II. Consistency and asymptotic normality. Bulletin of the Czech Econometric Society, no. 16, 1 - 28, 2002. Disadvantage of LTS non-increasingThe Least Weighted SquaresHence
relying on international trade The Czech Republic - small open economyThe export into EU increased in nineties from 8 billion US$ to 18.4 billion US$, i.e. annually 16.3%.
IN NUMBERS:Export into EU - 70.7 % 1/3 Germany 1/12 AustriaEuropean transition economies - 20.8 % 1/12 Slovakia 1/19 PolandRest of world - 8.4 %
HYPOTHESISThere is an increasing segment of economyIn other words:There is an increasing segment of economy - as follows from the previous - oriented on EU.which is export orientedwhich resembles market economy.
91 industries, nearly 40 variables, year 1994
X - export S - sales US - number of university students HS - number of high school studentsTFPW - total factor productivity related to wages DP - price development after opening-upFDI - foreigner direct investments VA - value addedW - wagesK - capitalBAL - Balasa indexIRS - increasing return from scaleR&D - research and developmentCR3 - market power (concentration)Pattern of variables The goal of analysis to find determinants of of the EXPORT and FDI DATA ABOUT THE CZECH ECONOMY
h=54 After a lot of experiments we arrived at the model SEARCHING FOR MODEL FOR EXPORT
Variablet-valuep-valueUS / VA0.1150.0215.2980.000003HS / VA0.1890.0394.8230.000016K / VA-0.2440.019-12.3550CR31.4860.3224.6100.000032TFPW-0.9790.227-4.3000.000088Bal0.2710.2021.3390.086866DP1.1800.1587.4670
Collecting results into the table .Subpopulations nested up to size 57 Selected subpopulationBreak in estimates of coefficientsLet us call it main subpopulation(8)(8)(7)(7)(9)(9)(8)
No of cases53545556575859US / VA0.1190.1150.1130.1060.1240.125-0.051HS / VA0.1870.1890.2010.1920.2030.4260.237K / VA-0.241-0.244-0.247-0.245-0.2510.330-0.233CR31.4041.4861.2741.3451.1531.1632.650TFPW-0.896-0.979-0.937-1.026-1.0180.302-1.661Balasa0.3720.2710.1060.0880.201-0.2090.589DP1.0971.1801.2441.2491.1020.7211.194R-squared0.8500.8530.8450.8310.8230.6360.650Chi-square10.34 7.357 9.937 8.331 9.921 26.3433.71
crude petroleum, natural gas (111+112), non-ferrous ores (120+132), sand, stones (141+142), chemicals, minerals (143-145), processing and preserving fruits and vegetables (153), animal oil, fats (154), dairy (155), grain mill products, starches (156), feeds (157), beverages, beers (159), textile fibre (171), textile products (175), knitted and crocheted products (177), leather clothes (181), other outwears (182), furs (183), leather dressing (191), bags, luggages (192), foot-wear (193), impreg-nation of wood (201), plywood and laminboard (202), wood-products (203-205), paper products (212), petroleum-processing (232), pharmacy, botanical products (244), man-made fibres (247),rubber (251), plastics (252), prod. of glass, ceramics (262), bricks and baked clay (264), cement, lime and plaster (265-266), cutting, s