Arias Castro, EryPateiro López, BeatrizRodríguez Casal, Alberto2019-04-152019-08-152018Ery Arias-Castro, Beatriz Pateiro-López & Alberto Rodríguez-Casal (2019) Minimax Estimation of the Volume of a Set Under the Rolling Ball Condition, Journal of the American Statistical Association, 114:527, 1162-1173, DOI: 10.1080/01621459.2018.14827510162-1459http://hdl.handle.net/10347/18629This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 2018, available online: http://www.tandfonline.com/10.1080/01621459.2018.1482751We 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 onlineeng© 2018 American Statistical AssociationMinimax lower boundr-convex hullRolling conditionSupport estimationVolume estimationjournal article10.1080/01621459.2018.14827511537-274Xopen access