uasa_a_1482751_sm5478.zip (229.91 kB)
Minimax Estimation of the Volume of a Set Under the Rolling Ball Condition
Version 3 2019-10-25, 13:13
Version 2 2018-08-16, 03:41
Version 1 2018-06-01, 19:19
dataset
posted on 2019-10-25, 13:13 authored by Ery Arias-Castro, Beatriz Pateiro-López, Alberto Rodríguez-CasalWe 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 α-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.