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Bootstrap Tests of Stochastic Dominance with AsymptoticSimilarity on the Boundary

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  • Oliver Linton
  • Kyungchul Song
  • Yoon-Jae Whang

Abstract

We propose a new method of testing stochastic dominance which improves onexisting tests based on bootstrap or subsampling. Our test requires estimation ofthe contact sets between the marginal distributions. Our tests have asymptoticsizes that are exactly equal to the nominal level uniformly over the boundarypoints of the null hypothesis and are therefore valid over the whole null hy-pothesis. We also allow the prospects to be indexed by in…nite as well as …nitedimensional unknown parameters, so that the variables may be residuals fromnonparametric and semiparametric models. Our simulation results show thatour tests are indeed more powerful than the existing subsampling and recenteredbootstrap.

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Bibliographic Info

Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2008/527.

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Date of creation: Feb 2008
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Handle: RePEc:cep:stiecm:/2008/527

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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

Related research

Keywords: Set estimation; Size of test; Unbiasedness; Similarity; Bootstrap; Subsampling.;

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  1. Donald W.K. Andrews, 1996. "A Conditional Kolmogorov Test," Cowles Foundation Discussion Papers 1111R, Cowles Foundation for Research in Economics, Yale University.
  2. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of semiparametric models when the criterion function is not smooth," LSE Research Online Documents on Economics 2167, London School of Economics and Political Science, LSE Library.
  3. Davidson, Russell & Duclos, Jean-Yves, 1998. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Cahiers de recherche 9805, Université Laval - Département d'économique.
  4. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-93, September.
  5. Horvath, Lajos & Kokoszka, Piotr & Zitikis, Ricardas, 2006. "Testing for stochastic dominance using the weighted McFadden-type statistic," Journal of Econometrics, Elsevier, vol. 133(1), pages 191-205, July.
  6. Koul, H. L. & Lahiri, S. N., 1994. "On Bootstrapping M-Estimated Residual Processes in Multiple Linear-Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 49(2), pages 255-265, May.
  7. Peter Hansen, 2003. "Asymptotic Tests of Composite Hypotheses," Working Papers 2003-09, Brown University, Department of Economics.
  8. Russell Davidson, 2006. "Stochastic Dominance," Departmental Working Papers 2006-19, McGill University, Department of Economics.
  9. Abadie A., 2002. "Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 284-292, March.
  10. Linton, Oliver & Maasoumi, Esfandiar & Whang, Yoon-Jae, 2003. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," SFB 373 Discussion Papers 2003,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  11. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, 09.
  12. Enno Mammen, . "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin.
  13. Whang, Yoon-Jae, 2000. "Consistent bootstrap tests of parametric regression functions," Journal of Econometrics, Elsevier, vol. 98(1), pages 27-46, September.
  14. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
  15. Y.K. Tse & Xibin Zhang, 2003. "A Monte Carlo Investigation of Some Tests for Stochastic Dominance," Monash Econometrics and Business Statistics Working Papers 7/03, Monash University, Department of Econometrics and Business Statistics.
  16. Kyungchul Song, 2008. "Testing Distributional Inequalities and Asymptotic Bias," PIER Working Paper Archive 08-005, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
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Cited by:
  1. Jesus Gonzalo & Jose Olmo, 2008. "Testing downside risk efficiency under market distress," Economics Working Papers we084321, Universidad Carlos III, Departamento de Economía.
  2. Jesús Gonzalo & José Olmo, 2009. "Downside Risk Efficiency Under Market Distress," Economics Working Papers we094423, Universidad Carlos III, Departamento de Economía.
  3. Huber, Martin & Mellace, Giovanni, 2011. "Testing instrument validity for LATE identification based on inequality moment constraints," Economics Working Paper Series 1143, University of St. Gallen, School of Economics and Political Science.
  4. Le-Yu Chen & Jerzy Szroeter, 2009. "Hypothesis testing of multiple inequalities: the method of constraint chaining," CeMMAP working papers CWP13/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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