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Asymptotic theory for maximum likelihood in nonparametric mixture models. (English) Zbl 1429.62117

Summary: 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.

MSC:

62G05 Nonparametric estimation
62F12 Asymptotic properties of parametric estimators
62G20 Asymptotic properties of nonparametric inference
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