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 ψopt. Moreover formulas for the asymptotic relative efficiency ARE(ψ2,ψ1) of the ψ2-test with respect to the ψ1-test are derived. It turns out that ψopt also yields the most efficient test in the sense that ARE(ψopt,ψ)≤1 for all (admissible) kernels ψ.
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Ferger, D. Maximal asymptotic power and efficiency of two-sample tests based on generalized U-Statistics. Metrika 60, 33–57 (2004). https://doi.org/10.1007/s001840300295
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DOI: https://doi.org/10.1007/s001840300295