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Bootstrap tests of stochastic dominance with asymptotic similarity on the boundary

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  • Oliver Linton

    ()
    (Institute for Fiscal Studies and London School of Economics)

  • Kyungchul Song
  • Yoon-Jae Whang

    (Institute for Fiscal Studies and Seoul National University)

Abstract

We propose a new method of testing stochastic dominance which improves on existing tests based on bootstrap or subsampling. Our test requires estimation of the contact sets between the marginal distributions. Our tests have asymptotic sizes that are exactly equal to the nominal level uniformly over the boundary points of the null hypothesis and are therefore valid over the whole null hypothesis. We also allow the prospects to be indexed by infinite as well as finite dimensional unknown parameters, so that the variables may be residuals from nonparametric and semiparametric models. Our simulation results show that our tests are indeed more powerful than the existing subsampling and recentered bootstrap.

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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP08/08.

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Date of creation: Mar 2008
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Handle: RePEc:ifs:cemmap:08/08

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  1. 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.
  2. Peter Hansen, 2003. "Asymptotic Tests of Composite Hypotheses," Working Papers 2003-09, Brown University, Department of Economics.
  3. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, 09.
  4. Hardle, W. & Mammen, E., 1990. "Comparing nonparametric versus parametric regression fits," CORE Discussion Papers 1990065, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. 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.
  6. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-93, September.
  7. 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.
  8. 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.
  9. Whang, Yoon-Jae, 2000. "Consistent bootstrap tests of parametric regression functions," Journal of Econometrics, Elsevier, vol. 98(1), pages 27-46, September.
  10. Russell Davidson, 2006. "Stochastic Dominance," Departmental Working Papers 2006-19, McGill University, Department of Economics.
  11. Donald W.K. Andrews, 1996. "A Conditional Kolmogorov Test," Cowles Foundation Discussion Papers 1111R, Cowles Foundation for Research in Economics, Yale University.
  12. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2005. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," Review of Economic Studies, Oxford University Press, vol. 72(3), pages 735-765.
  13. 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.
  14. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
  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. 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.
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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. 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.
  3. Jesús Gonzalo & José Olmo, 2009. "Downside Risk Efficiency Under Market Distress," Economics Working Papers we094423, Universidad Carlos III, Departamento de Economía.
  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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