Consistent Estimation of a Mixing Distribution
The Annals of Statistics · 1992 · Volume 20 · Issue 3
Abstract
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 identified 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 Simar.
Keywords
62F12; 62G05; maximum likelihood; maximum penalized likelihood; mixture distribution; Model selection;
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