Test on components of mixture densities

Florent Autin (1) , Christophe Pouet (2, 1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 ECM - École Centrale de Marseille

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 $Y_1, \dots, Y_n$ and $Z_1, \dots, Z_n$ 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.

Mots clés: Besov spaces; density estimation; minimax theory; mixture model; nonparametric tests; wavelet decomposition

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Florent Autin, Christophe Pouet. Test on components of mixture densities. Statistics & Risk Modeling with Applications in Finance and Insurance, 2011, 28 (4), pp.389-410. ⟨10.1524/strm.2011.1065⟩. ⟨hal-00438417v2⟩