  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 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.
