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

Gérard Biau, L. Györfi

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

We present two simple and explicit procedures for testing homogeneity of two independent multivariate samples of size n. The non-parametric 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 null 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 null distribution of the test statistic is obtained, leading to an asymptotically α-level test procedure.

Original languageEnglish
Pages (from-to)3965-3973
Number of pages9
JournalIEEE Transactions on Information Theory
Volume51
Issue number11
DOIs
Publication statusPublished - Nov 2005

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statistics
Statistics
Testing
homogeneity

Keywords

  • Central limit theorem
  • Consistent testing
  • Homogeneity testing
  • Large deviations
  • Partitions
  • Poissonization

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Information Systems

Cite this

On the asymptotic properties of a nonparametric L1-test statistic of homogeneity. / Biau, Gérard; Györfi, L.

In: IEEE Transactions on Information Theory, Vol. 51, No. 11, 11.2005, p. 3965-3973.

Research output: Contribution to journalArticle

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