The Annals of Statistics

Consistent Estimation of a Mixing Distribution

Brian G. Leroux

Full-text: Open access

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.

Article information

Source
Ann. Statist. Volume 20, Number 3 (1992), 1350-1360.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176348772

Digital Object Identifier
doi:10.1214/aos/1176348772

Mathematical Reviews number (MathSciNet)
MR1186253

Zentralblatt MATH identifier
0763.62015

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62F12: Asymptotic properties of estimators

Keywords
Mixture distribution maximum likelihood maximum penalized likelihood model selection

Citation

Leroux, Brian G. Consistent Estimation of a Mixing Distribution. Ann. Statist. 20 (1992), no. 3, 1350--1360. doi:10.1214/aos/1176348772. http://projecteuclid.org/euclid.aos/1176348772.


Export citation