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

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 hyp...

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Bibliographic Details
Published in:IEEE transactions on information theory 2005-11, Vol.51 (11), p.3965-3973
Main Authors: BIAU, Gérard, GYÖRFI, Laszlo
Format: Article
Language:English
Subjects:
Applied sciences
Asymptotic methods
Exact sciences and technology
Information theory
Information, signal and communications theory
Poisson distribution
Probability
Telecommunications and information theory
Tests
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Summary: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 alpha-level test procedure. [PUBLICATION ABSTRACT]
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2005.856979