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A Two-Sample Non-Parametric Likelihood Ratio Test

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  • Patrick Marsh

Abstract

This paper proposes a test for the hypothesis that two samples have the same distribution. The likelihood ratio test of Portnoy (1988) is applied in the context of the consistent series density estimator of Crain (1974) and Barron and Sheu (1991). It is proven that the test, when suitably standardised, is asymptotically standard normal and consistent against any complementary alternative. In comparison with the established Kolmogorov-Smirnov and Cramer-von Mises procedures the proposed test enjoys broadly comparable finite sample size properties, but vastly superior power properties.

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  • Patrick Marsh, "undated". "A Two-Sample Non-Parametric Likelihood Ratio Test," Discussion Papers 05/25, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:05/25
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    References listed on IDEAS

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    1. Gerda Claeskens & Nils Lid Hjort, 2004. "Goodness of Fit via Non‐parametric Likelihood Ratios," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 487-513, December.
    2. Marsh, Patrick, 2007. "Goodness of fit tests via exponential series density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2428-2441, February.
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    Cited by:

    1. L. Baringhaus & D. Kolbe, 2015. "Two-sample tests based on empirical Hankel transforms," Statistical Papers, Springer, vol. 56(3), pages 597-617, August.

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