Finite sample nonparametric inference and large sample efficiency
成果类型：
Article
署名作者：
Romano, JP; Wolf, M
署名单位：
Stanford University; Universidad Carlos III de Madrid
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
发表日期：
2000
页码：
756-778
关键词：
摘要：
Given a sample X-1,...,X-n from a distribution F, the problem of constructing nonparametric confidence intervals for the mean mu (F) is considered. Unlike bootstrap procedures or those based on normal approximations, we insist an any procedure being truly nonparametric in the sense that the probability that the confidence interval contains mu (F) based on a sample of size n from F be at least 1 - alpha for all F and all n. Bahadur and Savage proved it is impossible to find an effective (or bounded) confidence interval for mu (F) without some restrictions. Thus, we assume that F is supported on a known compact set, which we take to be [0, 1]. In this setting, an asymptotic efficiency result is obtained that gives a lower bound on the size of any conservative interval. We then provide a construction of an interval that meets our finite sample requirement on level, yet has an asymptotic efficiency property Thus, the price to be paid for using fully nonparametric procedures when considering the trade-off between exact inference statements and asymptotic efficiency is negligible. Much of what is accomplished for the mean generalizes to other settings as well.