On a L1-test statistic of homogeneity

Gérard Biau, László Györfi

Research output: Contribution to journalArticle


We present a simple and explicit multivariate procedure for testing homogeneity of two independent samples of size n. The test statistic T n is the L1 distance between the two empirical distributions restricted to a finite partition. We first discuss Chernoff-type large deviation properties of Tn. This results in a distribution-free strongly consistent test of homogeneity, which rejects the null if T n becomes large. Then the asymptotic null distribution of the test statistic is obtained, leading to a new consistent test procedure.

Original languageEnglish
Pages (from-to)877-881
Number of pages5
JournalBulletin of the Belgian Mathematical Society - Simon Stevin
Issue number5
Publication statusPublished - Dec 1 2006


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

ASJC Scopus subject areas

  • Mathematics(all)

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