RT Journal Article
T1 Minimax Estimation of the Volume of a Set Under the Rolling Ball Condition
A1 Arias Castro, Ery
A1 Pateiro López, Beatriz
A1 Rodríguez Casal, Alberto
K1 Minimax lower bound
K1 r-convex hull
K1 Rolling condition
K1 Support estimation
K1 Volume estimation
AB 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 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
PB Taylor & Francis
SN 0162-1459
YR 2018
FD 2018
LK http://hdl.handle.net/10347/18629
UL http://hdl.handle.net/10347/18629
LA eng
NO Ery 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: 10.1080/01621459.2018.1482751
NO This 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/10.1080/01621459.2018.1482751
NO This work was partially supported by the U.S. National Science Foundation (DMS 1513465) and by the Spanish Ministry of Economy and Competitiveness and ERDF funds (MTM2016-76969P)
DS Minerva
RD 29 abr 2026