A Two-sample Nonparametric Likelihood Ratio Test

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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, Cramer-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.

Original languageEnglish
Pages (from-to)1053-1065
Number of pages13
JournalJournal of Nonparametric Statistics
Issue number8
Publication statusPublished - 2011

Bibliographical note

M1 - 8


  • two sample tests
  • series density estimator
  • non-parametric likelihood ratio

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