The Annals of Statistics

Monte Carlo likelihood inference for missing data models

Yun Ju Sung and Charles J. Geyer

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 35, Number 3 (2007), 990-1011.

Dates
First available in Project Euclid: 24 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1185303995

Digital Object Identifier
doi:10.1214/009053606000001389

Mathematical Reviews number (MathSciNet)
MR2341695

Zentralblatt MATH identifier
1124.62009

Subjects
Primary: 62F12: Asymptotic properties of estimators
Secondary: 65C05: Monte Carlo methods

Keywords
Asymptotic theory Monte Carlo maximum likelihood generalized linear mixed model empirical process model misspecification

Citation

Sung, Yun Ju; Geyer, Charles J. Monte Carlo likelihood inference for missing data models. Ann. Statist. 35 (2007), no. 3, 990--1011. doi:10.1214/009053606000001389. https://projecteuclid.org/euclid.aos/1185303995


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