RT Journal Article
T1 A nonparametric approach to the estimation of lengths and surface areas
A1 Cuevas González, Antonio
A1 Fraiman, Ricardo
A1 Rodríguez Casal, Alberto
K1 Minkowski content
K1 Nonparametric set estimation
K1 Length estimation
K1 Statistical image analysis
AB The Minkowski content L0(G) of a body G⊂ℝd represents the boundary length (for d=2) or the surface area (for d=3) of G. A method for estimating L0(G) is proposed. It relies on a nonparametric estimator based on the information provided by a random sample (taken on a rectangle containing G) in which we are able to identify whether every point is inside or outside G. Some theoretical properties concerning strong consistency, L1-error and convergence rates are obtained. A practical application to a problem of image analysis in cardiology is discussed in some detail. A brief simulation study is provided
PB Institute of Mathematical Statistics
SN 0090-5364
YR 2007
FD 2007
LK http://hdl.handle.net/10347/18549
UL http://hdl.handle.net/10347/18549
LA eng
NO Cuevas, A., Fraiman, R., & Rodríguez-Casal, A. (2007). A nonparametric approach to the estimation of lengths and surface areas. The Annals Of Statistics, 35(3), 1031-1051. doi: 10.1214/009053606000001532
NO Supported in part by Spanish Grants. MTM2004-00098, MTM2005-00820 and PGIDIT06PXIB207009PR
DS Minerva
RD 30 abr 2026