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September, 1992 Consistent Estimation of a Mixing Distribution
Brian G. Leroux
Ann. Statist. 20(3): 1350-1360 (September, 1992). DOI: 10.1214/aos/1176348772


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.


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Brian G. Leroux. "Consistent Estimation of a Mixing Distribution." Ann. Statist. 20 (3) 1350 - 1360, September, 1992.


Published: September, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0763.62015
MathSciNet: MR1186253
Digital Object Identifier: 10.1214/aos/1176348772

Primary: 62G05
Secondary: 62F12

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.20 • No. 3 • September, 1992
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