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Maximal asymptotic power and efficiency of two-sample tests based on generalized U-Statistics

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  • Dietmar Ferger

Abstract

In this article a systematic study is given of the asymptotic behavior of two-sample tests based on U-Statistics with arbitrary antisymmetric kernels ψ. Besides the investigation under the hypothesis and under fixed alternatives we determine the local power as a function of ψ as well as its maximizing value ψ opt . Moreover formulas for the asymptotic relative efficiency ARE(ψ 2 ,ψ 1 ) of the ψ 2 -test with respect to the ψ 1 -test are derived. It turns out that ψ opt also yields the most efficient test in the sense that ARE(ψ opt ,ψ)≤1 for all (admissible) kernels ψ. Copyright Springer-Verlag 2004

Suggested Citation

  • Dietmar Ferger, 2004. "Maximal asymptotic power and efficiency of two-sample tests based on generalized U-Statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(1), pages 33-57, July.
    • Handle: RePEc:spr:metrik:v:60:y:2004:i:1:p:33-57
    DOI: 10.1007/s001840300295
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    Cited by:

    1. Marie Hušková & Simos Meintanis, 2008. "Tests for the multivariate -sample problem based on the empirical characteristic function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(3), pages 263-277.

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