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Testing for restricted stochastic dominance: some further results

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  • Russell Davidson

    () (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - CNRS - Centre National de la Recherche Scientifique - ECM - Ecole Centrale de Marseille, CIREG - Centre interuniversitaire de recherche en économie quantitative - Université de Montréal, Department of Economics - McGill University)

Abstract

Extensions are presented to the results of Davidson and Duclos (2007), whereby the null hypothesis of restricted stochastic non dominance can be tested by both asymptotic and bootstrap tests, the latter having considerably better properties as regards both size and power. In this paper, the methodology is extended to tests of higherorder stochastic dominance. It is seen that, unlike the first-order case, a numerical nonlinear optimisation problem has to be solved in order to construct the bootstrap DGP. Conditions are provided for a solution to exist for this problem, and efficient numerical algorithms are laid out. The empirically important case in which the samples to be compared are correlated is also treated, both for first-order and for higher-order dominance. For all of these extensions, the bootstrap algorithm is presented. Simulation experiments show that the bootstrap tests perform considerably better than asymptotic tests, and yield reliable inference in moderately sized samples.

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  • Russell Davidson, 2009. "Testing for restricted stochastic dominance: some further results," Working Papers halshs-00443556, HAL.
  • Handle: RePEc:hal:wpaper:halshs-00443556 Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00443556
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    References listed on IDEAS

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    7. David E. A. Giles, 2004. "Calculating a Standard Error for the Gini Coefficient: Some Further Results," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(3), pages 425-433, July.
    8. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
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    Cited by:

    1. George M. Constantinides & Michal Czerwonko & Stylianos Perrakis, 2017. "Mispriced Index Option Portfolios," NBER Working Papers 23708, National Bureau of Economic Research, Inc.
    2. Dirk Van de gaer & Joost Vandenbossche & José Luis Figueroa, 2014. "Children's Health Opportunities and Project Evaluation: Mexico's Oportunidades Program," World Bank Economic Review, World Bank Group, vol. 28(2), pages 282-310.
    3. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    4. Stengos, Thanasis & Thompson, Brennan S., 2012. "Testing for bivariate stochastic dominance using inequality restrictions," Economics Letters, Elsevier, vol. 115(1), pages 60-62.
    5. Yélé Maweki Batana & Jean-Yves Duclos, 2010. "Comparing Multidimensional Poverty with Qualitative Indicators of Well-Being," Cahiers de recherche 1004, CIRPEE.

    More about this item

    Keywords

    Higher-order stochastic dominance; empirical likelihood; bootstrap test; correlated samples;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty

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