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.
Publié le : 2007-01-14
Classification:
homogeneity testing,
partitions,
large deviations,
consistent testing,
central limit theorem,
Poissonization,
62G10
@article{1170347810,
author = {Biau, G\'erard and Gy\"orfi, L\'aszl\'o},
title = {On a $L\_1$-Test Statistic of Homogeneity},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {13},
number = {5},
year = {2007},
pages = { 877-881},
language = {en},
url = {http://dml.mathdoc.fr/item/1170347810}
}
Biau, Gérard; Györfi, László. On a $L_1$-Test Statistic of Homogeneity. Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, pp. 877-881. http://gdmltest.u-ga.fr/item/1170347810/