Test on components of mixture densities

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; this link had never been clearly established up to now.