Maximization by parts in likelihood inference

• 成果类型: Article
• 署名作者: Song, PXK; Fan, YQ; Kalbfleisch, JD
• 署名单位: University of Waterloo; Vanderbilt University; University of Michigan System; University of Michigan
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214505000000204
• 发表日期: 2005
• 页码: 1145-1158
• 关键词: linear mixed models; carlo maximum-likelihood; conditional duration; Robust Estimation; longitudinal data

摘要

This article presents and examines a new algorithm for solving a score equation for the maximum likelihood estimate in certain problems of practical interest. The method circumvents the need to compute second-order derivatives of the full likelihood function. It exploits the structure of certain models that yield a natural decomposition of a very complicated likelihood function. In this decomposition, the first part is a log-likelihood from a simply analyzed model, and the second part is used to update estimates from the first part. Convergence properties of this iterative (fixed-point) algorithm are examined, and asymptotics are derived for estimators obtained using only a finite number of iterations. Illustrative examples considered in the article include multivariate Gaussian copula models, nonnormal random-effects models, generalized linear mixed models, and state-space models. Properties of the algorithm and of estimators are evaluated in simulation studies on a bivariate copula model and a nonnormal linear random-effects model.