Monte Carlo likelihood inference for missing data models

• 成果类型: Article
• 署名作者: Sung, Yun Ju; Geyer, Charles J.
• 署名单位: Washington University (WUSTL); University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000001389
• 发表日期: 2007
• 页码: 990-1011
• 关键词: GENERALIZED LINEAR-MODELS; convex sets cones; maximum-likelihood; mixed models; em algorithm; CONVERGENCE; SEQUENCES; pedigrees

摘要

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 theta* 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 theta*. We give Logit-Normal generalized linear mixed model examples, calculated using an R package.