Cuevas González, AntonioFraiman, RicardoRodríguez Casal, Alberto2019-04-052019-04-052007Cuevas, 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: 10.1214/0090536060000015320090-5364http://hdl.handle.net/10347/18549The 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 providedeng© Institute of Mathematical Statistics, 2007Minkowski contentNonparametric set estimationLength estimationStatistical image analysisjournal article10.1214/009053606000001532open access