On profile likelihood

• 成果类型: Article
• 署名作者: Murphy, SA; Van der Vaart, AW
• 署名单位: University of Michigan System; University of Michigan; Vrije Universiteit Amsterdam
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2669386
• 发表日期: 2000
• 页码: 449-465
• 关键词: doubly censored-data; proportional odds regression; asymptotic properties; large sample; survival function; hazards model; frailty model; Consistency; estimators; CONVERGENCE

摘要

We show that semiparametric profile likelihoods, where the nuisance parameter has been profiled out, behave like ordinary likelihoods in that they have a quadratic expansion. In this expansion the score function and the Fisher information are replaced by-the efficient score function and efficient Fisher information. The expansion may be used, among others, to prove the asymptotic normality of the maximum likelihood estimator, to derive the asymptotic chi-squared distribution of the log-likelihood ratio statistic, and to prove the consistency of the observed information as an estimator of the inverse of the asymptotic variance.