Minimax Estimation of the Volume of a Set Under the Rolling Ball Condition

• 成果类型: Article
• 署名作者: Arias-Castro, Ery; Pateiro-Lopez, Beatriz; Rodriguez-Casal, Alberto
• 署名单位: University of California System; University of California San Diego; Universidade de Santiago de Compostela
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2018.1482751
• 发表日期: 2019
• 页码: 1162-1173
• 关键词: surface-area estimation; shape; confidence; perimeter; MODEL

摘要

We consider the problem of estimating the volume of a compact domain in a Euclidean space based on a uniform sample from the domain. We assume that the domain has a boundary with positive reach. We propose a data-splitting approach to correct the bias of the plug-in estimator based on the sample alpha-convex hull. We show that this simple estimator achieves a minimax lower bound that we derive. Some numerical experiments corroborate our theoretical findings. Supplementary materials for this article are available online.