Tests on components of density mixtures

TL;DR

This paper introduces an asymptotically optimal statistical test to determine if two independent samples originate from the same mixture of components, with detailed analysis of mixing weights and numerical validation.

Contribution

It proposes a new testing procedure for mixture components that is proven to be asymptotically optimal in a minimax framework.

Findings

Test procedure is asymptotically minimax optimal.

Performance depends on mixing weights.

Numerical examples illustrate effectiveness.

Abstract

This paper deals with statistical tests on the components of mixture densities. We propose to test whether the densities of two independent samples of independent random variables $Y_1, ..., Y_n$ and $Z_1, ..., Z_n$ result from the same mixture of $M$ components or not. We provide a test procedure which is proved to be asymptotically optimal according to the minimax setting. We extensively discuss the connection between the mixing weights and the performance of the testing procedure and illustrate it with numerical examples.