Asymptotically efficient estimation in the Wicksell problem

• 成果类型: Article
• 署名作者: Golubev, GK; Levit, BY
• 署名单位: Russian Academy of Sciences; Utrecht University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 2407-2419
• 关键词: sphere size distributions

摘要

We consider the classical Wicksell problem of estimating an unknown distribution function G of the radii of balls, based on their observed cross-sections. It is assumed that the underlying distribution function G belongs to a Holder class of smoothness gamma > 1/2. We prove that, for a suitable choice of the smoothing parameters, kernel-type estimators are asymptotically efficient for a large class of symmetric bowl-shaped loss functions.