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A two-sample nonparametric likelihood ratio test

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  • Patrick Marsh

Abstract

This paper proposes a new test for the hypothesis that two samples have the same distribution. The likelihood ratio test of Portnoy [Portnoy, S. (1988), ‘Asymptotic Behaviour of Likelihood Methods for Exponential Families When the Number of Parameters Tends to Infinity’, Annals of Statistics, 16, 356–366] is applied in the context of the consistent series density estimator of Crain [Crain, B.R. (1974), ‘Estimation of Distributions Using Orthogonal Expansions’, Annals of Statistics, 2, 454–463] and Barron and Sheu [Barron, A.R., and Sheu, C.-H. (1991), ‘Approximation of Density Functions by Sequences of Exponential Families’. Annals of Statistics, 19, 1347–1369]. It is proven that the test, when suitably standardised, is asymptotically standard normal and consistent against any complementary fixed alternative. In comparison with established tests, such as the Kolmogorov–Smirnov, Cramér-von Mises and rank sum, median, and dispersion tests, the proposed tests enjoy broadly comparable finite sample size properties, but vastly superior power properties when considered over a range of different alternatives.

Suggested Citation

  • Patrick Marsh, 2010. "A two-sample nonparametric likelihood ratio test," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(8), pages 1053-1065.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:8:p:1053-1065
    DOI: 10.1080/10485250903486078
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    References listed on IDEAS

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    1. Marsh, Patrick, 2007. "Goodness of fit tests via exponential series density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2428-2441, February.
    2. 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.
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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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