Asymptotic theory for maximum likelihood in nonparametric mixture models

Authors:
Sara van de Geer
Affiliations:
Mathematical Institute, University of Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands
Venue:
Computational Statistics & Data Analysis
Year:
2003

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Abstract

An overview of asymptotic results is presented for the maximum likelihood estimator in mixture models. The mixing distribution is assumed to be completely unknown, so that the model considered is nonparametric. Conditions for consistency, rates of convergence and asymptotic efficiency are provided. Examples include convolution models, and the case of piecewise monotone densities.