2016/05/04 by Ery Arias-Castro, Arias-Castro, Ery, Beatriz Pateiro‐López +3
Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning and Algorithms #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1605.01333
openalex publication_date 2016/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.