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On a L1-Test Statistic of Homogeneity

On a L1-Test Statistic of Homogeneity

This video was recorded at NIPS Workshop on Representations and Inference on Probability Distributions, Whistler 2007. My presentation will be divided in two parts. First, I will present two simple and explicit procedures for testing homogeneity of two independent multivariate samples of size $n$. The nonparametric tests are based on the statistic $T_n$, which is the $L_1$ distance between the two empirical distributions restricted to a finite partition. Both tests reject the null hypothesis of homogeneity if $T_n$ becomes large, i.e., if $T_n$ exceeds a threshold. I will first discuss Chernoff-type large deviation properties of $T_n$. This results in a distribution-free strong consistent test of homogeneity. Then the asymptotic null distribution of the test statistic is obtained, leading... Show More

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