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A Kolmogorov-type test for second-order stochastic dominance

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  • Schmid, Friedrich
  • Trede, Mark

Abstract

A nonparametric test for second-order stochastic dominance is introduced in the framework of the one sample problem. It is based on a supremum statistic which is suitable for second-order problems. Its asymptotic distribution is identified and quantiles of the finite sample and asymptotic distributions are derived by simulations. Its power is compared to those of a test suggested by Deshpande and Singh (1985) which is based on an integral statistic. Finally, it is shown that the new test can also be used for testing first order stochastic dominance. A family of alternatives is given where the second-order test has uniformly higher power than the usual first-order Kolmogorov test.

Suggested Citation

  • Schmid, Friedrich & Trede, Mark, 1998. "A Kolmogorov-type test for second-order stochastic dominance," Statistics & Probability Letters, Elsevier, vol. 37(2), pages 183-193, February.
    • Handle: RePEc:eee:stapro:v:37:y:1998:i:2:p:183-193
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    References listed on IDEAS

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    1. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    2. Schmid, Friedrich & Trede, Mark, 1996. "Nonparametric inference for second order stochastic dominance," Discussion Papers in Econometrics and Statistics 2/96, University of Cologne, Institute of Econometrics and Statistics.
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