On nonparametric confidence intervals
成果类型：
Article
署名作者：
Low, MG
署名单位：
University of Pennsylvania
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
发表日期：
1997
页码：
2547-2554
关键词：
摘要：
An inequality is given for the expected length of a confidence interval given that a particular distribution generated the data and assuming that the confidence interval has a given coverage probability over a family of distributions. As a corollary, attempts to adapt to the regularity of the true density within derivative smoothness classes cannot improve the rate of convergence of the length of the confidence interval over minimax fixed-length intervals and still maintain uniform coverage probability. However, adaptive confidence intervals can attain improved rates of convergence in some other classes of densities, such as those satisfying a shape restriction.