Leroux, Brian G. Consistent estimation of a mixing distribution. (English) Zbl 0763.62015 Ann. Stat. 20, No. 3, 1350-1360 (1992). 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)]. Cited in 2 ReviewsCited in 115 Documents MSC: 62G05 Nonparametric estimation 62F12 Asymptotic properties of parametric estimators Keywords:maximum-penalized-likelihood method; weak convergence; new proof; consistency of maximum-likelihood estimators; large-sample limits of estimators; minimizing Kullback-Leibler divergence; Poisson mixture distribution Citations:Zbl 0362.62095 PDFBibTeX XMLCite \textit{B. G. Leroux}, Ann. Stat. 20, No. 3, 1350--1360 (1992; Zbl 0763.62015) Full Text: DOI