A Kiefer-Wolfowitz comparison theorem for wicksell's problem
成果类型：
Article
署名作者：
Wang, Xiao; Woodroofe, Michael
署名单位：
University System of Maryland; University of Maryland Baltimore County; University of Michigan System; University of Michigan
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/009053606000001604
发表日期：
2007
页码：
1559-1575
关键词：
摘要：
We extend the isotonic analysis for Wicksell's problem to estimate a regression function, which is motivated by the problem of estimating dark matter distribution in astronomy. The main result is a version of the Kiefer-Wolfowitz theorem comparing the empirical distribution to its least concave majorant, but with a convergence rate n(-1) log n faster than n(-2/3) log n. The main result is useful in obtaining asymptotic distributions for estimators, such as isotonic and smooth estimators.