The Annals of Statistics
- Ann. Statist.
- Volume 20, Number 3 (1992), 1350-1360.
Consistent Estimation of a Mixing Distribution
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.
Ann. Statist., Volume 20, Number 3 (1992), 1350-1360.
First available in Project Euclid: 12 April 2007
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Leroux, Brian G. Consistent Estimation of a Mixing Distribution. Ann. Statist. 20 (1992), no. 3, 1350--1360. doi:10.1214/aos/1176348772. https://projecteuclid.org/euclid.aos/1176348772