Existence and consistency of maximum likelihood in upgraded mixture models. (English) Zbl 0752.62026

van der Vaart, A. W.; Wellner, Jon A.

J. Multivariate Anal. 43, No. 1, 133-146 (1992).

Summary: Suppose one observes a sample of size \(m\) from the mixture density \(\int p(x\mid z)d\eta(z)\) and a sample of size \(n\) from the distribution \(\eta\). The kernel \(p(x\mid z)\) is known. We show existence of the maximum likelihood estimator for \(\eta\), characterize its support, and prove consistency as \(m\), \(n\to\infty\).

MSC:

62F12	Asymptotic properties of parametric estimators
62G20	Asymptotic properties of nonparametric inference

Keywords:

upgraded mixture models; mixture density; existence of the maximum likelihood estimators; support; consistency

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