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Asymptotic normality in mixture models

Published online by Cambridge University Press:  15 August 2002

Sara Van De Geer
Sara Van De Geer*
Affiliation:
University of Leiden, Netherlands
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Abstract

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 of F and the NPMLE.

Keywords

Asymptotic efficiency / asymptotic normality / differentiable functionals / maximum likelihood / mixture model.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 1 , 1997 , pp. 17 - 33
Copyright
© EDP Sciences, SMAI, 1997

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