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December, 1984 Asymptotic Properties of Maximum Likelihood Estimates in the Mixed Poisson Model
Diane Lambert, Luke Tierney
Ann. Statist. 12(4): 1388-1399 (December, 1984). DOI: 10.1214/aos/1176346799


This paper considers the asymptotic behavior of the maximum likelihood estimators (mle's) of the probabilities of a mixed Poisson distribution with a nonparametric mixing distribution. The vector of estimated probabilities is shown to converge in probability to the vector of mixed probabilities at rate $n^{1/2-\varepsilon}$ for any $\varepsilon > 0$ under a generalized $\chi^2$ distance function. It is then shown that any finite set of the mle's has the same joint limiting distribution as does the corresponding set of sample proportions when the support of the mixing distribution $G_0$ is an infinite set with a known upper bound and $G_0$ satisfies a certain condition at zero.


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Diane Lambert. Luke Tierney. "Asymptotic Properties of Maximum Likelihood Estimates in the Mixed Poisson Model." Ann. Statist. 12 (4) 1388 - 1399, December, 1984.


Published: December, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0562.62038
MathSciNet: MR765931
Digital Object Identifier: 10.1214/aos/1176346799

Primary: 62E20
Secondary: 62G05

Keywords: asymptotic normality , consistency , nonparametric maximum likelihood estimation

Rights: Copyright © 1984 Institute of Mathematical Statistics


Vol.12 • No. 4 • December, 1984
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