### Abstract

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 L_{1} distance between the two empirical distributions restricted to a finite partition. We first discuss Chernoff-type large deviation properties of T_{n}. 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 language | English |
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Pages (from-to) | 877-881 |

Number of pages | 5 |

Journal | Bulletin of the Belgian Mathematical Society - Simon Stevin |

Volume | 13 |

Issue number | 5 |

Publication status | Published - Dec 1 2006 |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Biau, G., & Györfi, L. (2006). On a L

_{1}-test statistic of homogeneity.*Bulletin of the Belgian Mathematical Society - Simon Stevin*,*13*(5), 877-881.