Christophe Pouet: Varying mixing weights model

The varying mixing weights model was introduced by Maiboroda. Contrary to the usual mixture models, this model is identifiable even when nonparametric density functions are considered. In this talk, I will give a broad range of results for hypothesis testing problems under the varying mixing weights model. First, I will motivate the problem with some real data. Then I will give theoretical results in the minimax framework. The effect of the smallest eigenvalue of a matrix linked to the varying mixing weights will be discussed in details. We will see that in some asymptotic setting it can lead to new rates of hypothesis testing. This talk is based on several joined works with Florent Autin (Aix-Marseille Universite).