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Bootstrap Tests of Stochastic Dominance with AsymptoticSimilarity on the Boundary

  • Oliver Linton
  • Kyungchul Song
  • Yoon-Jae Whang

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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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
Contact details of provider: Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

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  1. Donald W. K. Andrews, 1997. "A Conditional Kolmogorov Test," Econometrica, Econometric Society, vol. 65(5), pages 1097-1128, September.
  2. 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.
  3. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-93, September.
  4. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function is not Smooth," STICERD - Econometrics Paper Series /2003/450, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  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. Davidson, R. & Duclos, J.-Y., 1998. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," G.R.E.Q.A.M. 98a14, Universite Aix-Marseille III.
  7. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
  8. Russell Davidson, 2006. "Stochastic Dominance," Departmental Working Papers 2006-19, McGill University, Department of Economics.
  9. Whang, Yoon-Jae, 2000. "Consistent bootstrap tests of parametric regression functions," Journal of Econometrics, Elsevier, vol. 98(1), pages 27-46, September.
  10. Enno Mammen, . "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin.
  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. 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.
  13. Peter Hansen, 2003. "Asymptotic Tests of Composite Hypotheses," Working Papers 2003-09, Brown University, Department of Economics.
  14. 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.
  15. 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.
  16. 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.
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