## Bulletin of the Belgian Mathematical Society - Simon Stevin

- Bull. Belg. Math. Soc. Simon Stevin
- Volume 13, Number 5 (2007), 877-881.

### On a $L_1$-Test Statistic of Homogeneity

#### 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.

#### Article information

**Source**

Bull. Belg. Math. Soc. Simon Stevin, Volume 13, Number 5 (2007), 877-881.

**Dates**

First available in Project Euclid: 1 February 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.bbms/1170347810

**Mathematical Reviews number (MathSciNet)**

MR2293214

**Zentralblatt MATH identifier**

1116.62048

**Subjects**

Primary: 62G10: Hypothesis testing

**Keywords**

homogeneity testing partitions large deviations consistent testing central limit theorem Poissonization

#### Citation

Biau, Gérard; Györfi, László. On a $L_1$-Test Statistic of Homogeneity. Bull. Belg. Math. Soc. Simon Stevin 13 (2007), no. 5, 877--881. https://projecteuclid.org/euclid.bbms/1170347810