Asymptotic normality in mixture models
Sara Van De Geer (2010)
ESAIM: Probability and Statistics
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We study the estimation of a linear integral functional of a distribution F, using i.i.d. observations which density is a mixture of a family of densities k(.,y) under F. We examine the asymptotic distribution of the estimator obtained by plugging the non parametric maximum likelihood estimator (NPMLE) of F in the functional. A problem here is that usually, the NPMLE does not dominate F. Our main aim here is to show that this can be overcome by considering a convex combination...