Asymptotic normality in mixture models

Abstract

We study the estimation of a linear function θ0 = ∫adF0 of a distribution F0, using i.I.D. observations of the mixture pF0 = ∫ k(·, y)dF0(y). Let Fn be the maximum likelihood estimator of F0 and θ = ∫adFn. We examine the asymptotic distribution of Fn. A problem here is that usually, Fn does not dominate F0. Our main aim is to show that this can be overcome by considering the convex combination αFn + (1 – α)F0, with α < 1. © 1995 EDP Sciences.