On the asymptotic properties of a nonparametric L1-test statistic of homogeneity

Authors:
G. Biau;L. Gyorfi
Affiliations:
Inst. de Math., Univ. Montpellier, France;-
Venue:
IEEE Transactions on Information Theory
Year:
2005

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Abstract

We present two simple and explicit procedures for testing homogeneity of two independent multivariate samples of size n. The nonparametric tests are based on the statistic Tn, which is the L1 distance between the two empirical distributions restricted to a finite partition. Both tests reject the hypothesis of homogeneity if Tn becomes large, i.e., if Tn exceeds a threshold. We first discuss Chernoff-type large deviation properties of Tn. This results in a distribution-free strong consistent test of homogeneity. Then the asymptotic distribution of the test statistic is obtained, leading to an asymptotically α-level test procedure.