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An Improved Bootstrap Test of Stochastic Dominance

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Author Info

  • Oliver Linton

    (London School of Economics)

  • Kyungchul Song

    (University of Pennsylvania)

  • Yoon-Jae Whang

    (Seoul National University)

Abstract

We propose a new method of testing stochastic dominance that improves on existing tests based on the standard bootstrap or subsampling. The method admits prospects involving infinite as well as finite dimensional unknown parameters, so that the variables are allowed to be residuals from nonparametric and semiparametric models. The proposed bootstrap tests have asymptotic sizes that are less than or equal to the nominal level uniformly over probabilities in the null hypothesis under regularity conditions. This paper also characterizes the set of probabilities that the asymptotic size is exactly equal to the nominal level uniformly. As our simulation results show, these characteristics of our tests lead to an improved power property in general. The improvement stems from the design of the bootstrap test whose limiting behavior mimics the discontinuity of the original test's limiting distribution.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1713.

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Length: 43 pages
Date of creation: Jul 2009
Date of revision:
Publication status: Published in Journal of Econometrics (February 2010), 154(2): 186-202
Handle: RePEc:cwl:cwldpp:1713

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Phone: (203) 432-3702
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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

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References

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  1. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
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  5. Xiaohong Chen & Oliver Linton & Ingred Van Keilegom, 2002. "Estimation of semiparametric models when the criterion function is not smooth," CeMMAP working papers CWP02/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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  12. 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.
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  17. Heckman, James J & Ichimura, Hidehiko & Todd, Petra, 1998. "Matching as an Econometric Evaluation Estimator," Review of Economic Studies, Wiley Blackwell, vol. 65(2), pages 261-94, April.
  18. Andrews, Donald W.K. & Guggenberger, Patrik, 2010. "ASYMPTOTIC SIZE AND A PROBLEM WITH SUBSAMPLING AND WITH THE m OUT OF n BOOTSTRAP," Econometric Theory, Cambridge University Press, vol. 26(02), pages 426-468, April.
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Citations

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Cited by:
  1. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, 03.
  2. Chia-Lin Chang & Juan-Ángel Jiménez-Martín & Esfandiar Maasoumi & Teodosio Pérez Amaral, 2014. "A Stochastic Dominance Approach to Financial Risk Management Strategies," Documentos de Trabajo del ICAE 2014-08, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico, revised Apr 2014.
  3. Le-Yu Chen & Jerzy Szroeter, 2012. "Testing multiple inequality hypotheses: a smoothed indicator approach," CeMMAP working papers CWP16/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Sokbae 'Simon' Lee & Yoon-Jae Whang, 2009. "Nonparametric tests of conditional treatment effects," CeMMAP working papers CWP36/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Stephen G. Donald & Yu-Chin Hsu, 2012. "Estimation and Inference for Distribution Functions and Quantile Functions in Treatment Effect Models," IEAS Working Paper : academic research 12-A016, Institute of Economics, Academia Sinica, Taipei, Taiwan.
  6. Christopher J. Bennett & Ričardas Zitikis, 2013. "Examining the Distributional Effects of Military Service on Earnings: A Test of Initial Dominance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 1-15, January.
  7. Sokbae Lee & Kyungchul Song & Yoon-Jae Whang, 2014. "Testing For A General Class Of Functional Inequalities," KIER Working Papers 889, Kyoto University, Institute of Economic Research.
  8. Fan, Yanqin & Park, Sang Soo, 2012. "Confidence intervals for the quantile of treatment effects in randomized experiments," Journal of Econometrics, Elsevier, vol. 167(2), pages 330-344.
  9. Kyungchul Song, 2009. "Testing Predictive Ability and Power Robustification," PIER Working Paper Archive 09-035, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  10. Oliver Linton & Yoon-Jae Whang & Yu-Min Yen, 2012. "A nonparametric test of the leverage hypothesis," CeMMAP working papers CWP24/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  11. Donald W.K. Andrews & Xu Cheng & Patrik Guggenberger, 2011. "Generic Results for Establishing the Asymptotic Size of Confidence Sets and Tests," Cowles Foundation Discussion Papers 1813, Cowles Foundation for Research in Economics, Yale University.
  12. Toru Kitagawa, 2013. "A bootstrap test for instrument validity in heterogeneous treatment effect models," CeMMAP working papers CWP53/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  13. Miguel A. Delgado & Juan Carlos Escanciano, 2013. "Conditional Stochastic Dominance Testing," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 16-28, January.
  14. Fan, Yanqin & Park, Sang Soo, 2014. "Nonparametric inference for counterfactual means: Bias-correction, confidence sets, and weak IV," Journal of Econometrics, Elsevier, vol. 178(P1), pages 45-56.
  15. Khan, Shakeeb & Ponomareva, Maria & Tamer, Elie, 2011. "Identification of Panel Data Models with Endogenous Censoring," MPRA Paper 30373, University Library of Munich, Germany.

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