A nonparametric approach to the estimation of lengths and surface areas

• 成果类型: Article
• 署名作者: Cuevas, Antonio; Fraiman, Ricardo; Rodriguez-Casal, Alberto
• 署名单位: Autonomous University of Madrid; Universidade de Santiago de Compostela
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000001532
• 发表日期: 2007
• 页码: 1031-1051
• 关键词: level sets; support

摘要

The Minkowski content L-0(G) of a body G C R-d represents the bound ary length (for d = 2) or the surface area (for d = 3) of G. A method for estimating L-0(G) is proposed. It relies on a nonparametric estimator based on the information provided by a random sample (taken on a rectangle containing G) in which we are able to identify whether every point is inside or outside G. Some theoretical properties concerning strong consistency, L-1-error and convergence rates are obtained. A practical application to a problem of image analysis in cardiology is discussed in some detail. A brief simulation study is provided.