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.
Citation
Gérard Biau. László Györfi. "On a $L_1$-Test Statistic of Homogeneity." Bull. Belg. Math. Soc. Simon Stevin 13 (5) 877 - 881, January 2007. https://doi.org/10.36045/bbms/1170347810
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