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Consistent estimation of a mixing distribution. (English) Zbl 0763.62015

Summary: A maximum-penalized-likelihood method is proposed for estimating a mixing distribution and it is shown that this method produces a consistent estimator, in the sense of weak convergence. In particular, a new proof of the consistency of maximum-likelihood estimators is given. The estimated number of components is shown to be at least as large as the true number, for large samples. Also, the large-sample limits of estimators which are constrained to have a fixed finite number of components are identifed as distributions minimizing Kullback-Leibler divergence from the true mixing distribution. Estimation of a Poisson mixture distribution is illustrated using the distribution of traffic accidents presented by L. Simar [ibid. 4, 1200-1209 (1976; Zbl 0362.62095)].

MSC:

62G05 Nonparametric estimation
62F12 Asymptotic properties of parametric estimators

Citations:

Zbl 0362.62095
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