Sequential confidence regions for maximum likelihood estimates

• 成果类型: Article
• 署名作者: Dmitrienko, A; Govindarajulu, Z
• 署名单位: Eli Lilly; Lilly Research Laboratories; University of Kentucky
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2000
• 页码: 1472-1501
• 关键词: asymptotic properties; logistic-regression; spearman-karber; renewal theory; accuracy; LAW

摘要

The goal of this paper is ti,develop a general framework for constructing sequential fixed size confidence regions based on maximum likelihood estimates. Asymptotic properties of the sequential procedure for setting up the confidence regions are analyzed under very broad assumptions on the underlying parametric model. It is shown that the proposed sequential procedure is asymptotically optimal in the sense that it approximates the optimal fixed-sample size procedure. It is further shown that the cost of ignorance associated with the sequential procedure is bounded. Applications are made to estimation problems arising in prospective and retrospective studies.