MINIMUM HELLINGER DISTANCE ESTIMATION OF PARAMETER IN THE RANDOM CENSORSHIP MODEL

• 成果类型: Article
• 署名作者: YANG, S
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348112
• 发表日期: 1991
• 页码: 579-602
• 关键词: product-limit estimator; robust

摘要

This paper discusses the minimum Hellinger distance estimation (MHDE) of the parameter that gives the best fit of a parametric family to a density when the data are randomly censored. In studying the MHDE, the tail behavior of the product-limit (P-L) process is investigated, and the weak convergence of the process on the real line is established. An upper bound on the mean square increment of the normalized P-L process is also obtained. With these results, the asymptotic behavior of the MHDE is established and it is shown that, when the parametric model is correct, the MHD estimators are asymptotically efficient among the class of regular estimators. This estimation procedure is also minimax robust in small Hellinger neighbourhoods of the given parametric family. The work extends the results of Beran for the complete i.i.d. data case to the censored data case. Some of the proofs employ the martingale techniques by Gill.