Marginal likelihood, conditional likelihood and empirical likelihood: Connections and applications

• 成果类型: Article
• 署名作者: Qin, J; Zhang, B
• 署名单位: National Institutes of Health (NIH) - USA; NIH National Institute of Allergy & Infectious Diseases (NIAID); University System of Ohio; University of Toledo
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/92.2.251
• 发表日期: 2005
• 页码: 251270
• 关键词: confidence-intervals; regression-models; DISCRIMINATION; distributions

摘要

Marginal likelihood and conditional likelihood are often used for eliminating nuisance parameters. For a parametric model, it is well known that the full likelihood can be decomposed into the product of a conditional likelihood and a marginal likelihood. This property is less transparent in a nonparametric or semiparametric likelihood setting. In this paper we show that this nice parametric likelihood property can be carried over to the empirical likelihood world. We discuss applications in case-control studies, genetical linkage analysis, genetical quantitative traits analysis, tuberculosis infection data and unordered-paired data, all of which can be treated as semiparametric finite mixture models. We consider the estimation problem in detail in the simplest case of unordered-paired data where we can only observe the minimum and maximum values of two random variables; the identities of the minimum and maximum values are lost. The profile empirical likelihood approach is used for maximum semiparametric likelihood estimation. We present some large-sample results along with a simulation study.