Non-asymptotic detection of two-component mixtures with unknown means

Abstract

This work is concerned with the detection of a mixture distribution from a R-valued sample. More precisely, given observations X1, …, Xn, our aim is to detect whether the corresponding distribution is g (up to a translation) or is defined as a two-component mixture. We propose a non-asymptotic testing procedure and determine conditions for which the power of the test can be controlled for a prescribed level. In a second time, we investigate the performances of our algorithm in a 'benchmark' asymptotic setting.