Isotonic estimation and rates of convergence in Wicksell's problem
成果类型：
Article
署名作者：
Groeneboom, P; Jongbloed, G
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176324310
发表日期：
1995
页码：
1518-1542
关键词：
摘要：
It is shown that, in the nonparametric setting for the so-called Wicksell problem, the distribution function of the squared radii of the balls cannot be estimated at a rate faster than n(-1/2)root log n. We present an isotonic estimator of the distribution function which attains this rate and derive its asymptotic (normal) distribution. It is shown that the variance of this limiting distribution is exactly half the asymptotic variance of the naive plug-in estimator.