ON MAXIMUM-LIKELIHOOD-ESTIMATION IN INFINITE DIMENSIONAL PARAMETER SPACES

• 成果类型: Article
• 署名作者: WONG, WH; SEVERINI, TA
• 署名单位: Northwestern University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348113
• 发表日期: 1991
• 页码: 603-632
• 关键词: convergence; EFFICIENCY; models; INFORMATION; rates

摘要

An approximate maximum likelihood estimate is known to be consistent under some compactness and integrability conditions. In this paper we study its convergence rate and its asymptotic efficiency in estimating smooth functionals of the parameter. We provide conditions under which the rate of convergence can be established. This rate is essentially governed by the size of the space of score functions as measured by an entropy index. We also show that, for a large class of smooth functionals, the plug-in maximum likelihood estimate is asymptotically efficient, that is, it achieves the minimal Fisher information bound. The theory is illustrated by several nonparametric or semiparametric examples.