ON OPTIMAL B-ROBUST INFLUENCE FUNCTIONS IN SEMIPARAMETRIC MODELS

• 成果类型: Article
• 署名作者: SHEN, LZ
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176324631
• 发表日期: 1995
• 页码: 968-989
• 关键词: partial likelihood estimators; EFFICIENCY

摘要

Bounded influence functions are used for robust estimation in semiparametric models. In this paper, we generalize Hampel's variational problem to semiparametric models and define the optimal B-robust influence function as the one solving the variational problem. We identify the lowest bounds for influence functions and establish the existence and uniqueness of the optimal influence functions in general semiparametric models. Explicit optimal influence functions are given for a special case. Examples are provided to illustrate the procedures for calculating the optimal influence functions and for constructing the corresponding optimal estimators.