Open Access
July 2007 Monte Carlo likelihood inference for missing data models
Yun Ju Sung, Charles J. Geyer
Ann. Statist. 35(3): 990-1011 (July 2007). DOI: 10.1214/009053606000001389


We describe a Monte Carlo method to approximate the maximum likelihood estimate (MLE), when there are missing data and the observed data likelihood is not available in closed form. This method uses simulated missing data that are independent and identically distributed and independent of the observed data. Our Monte Carlo approximation to the MLE is a consistent and asymptotically normal estimate of the minimizer θ* of the Kullback–Leibler information, as both Monte Carlo and observed data sample sizes go to infinity simultaneously. Plug-in estimates of the asymptotic variance are provided for constructing confidence regions for θ*. We give Logit–Normal generalized linear mixed model examples, calculated using an R package.


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Yun Ju Sung. Charles J. Geyer. "Monte Carlo likelihood inference for missing data models." Ann. Statist. 35 (3) 990 - 1011, July 2007.


Published: July 2007
First available in Project Euclid: 24 July 2007

zbMATH: 1124.62009
MathSciNet: MR2341695
Digital Object Identifier: 10.1214/009053606000001389

Primary: 62F12
Secondary: 65C05

Keywords: Asymptotic theory , empirical process , Generalized linear mixed model , maximum likelihood , model misspecification , Monte Carlo

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 3 • July 2007
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