Title: Multidimensional two-component Gaussian mixtures detection
Authors: Clement Marteau - Université Lyon 1 (France) [presenting]
Abstract: Let $(X_1,\ldots,X_n)$ be a $d$-dimensional i.i.d sample from a distribution with density $f$. The problem of detection of a two-component mixture is considered. The aim is to decide whether $f$ is the density of a standard Gaussian random $d$-vector ($f=\phi_d$) against $f$ is a two-component mixture. Optimal separation conditions on the mixture parameters and the dimension $d$ are established, allowing to separate both hypotheses with prescribed errors. Several testing procedures are proposed and two alternative subsets are considered. The inverse problem and direct problem point of view will also be briefly discussed.