A nonparametric approach to the estimation of lengths and surface areas
| dc.creator | Cuevas, Antonio | |
| dc.creator | Fraiman, Ricardo | |
| dc.creator | Rodríguez-Casal, Alberto | |
| dc.date | 2007-08-16 | |
| dc.date.accessioned | 2026-07-07T08:24:38Z | |
| dc.date.available | 2026-07-07T08:24:38Z | |
| dc.description | The Minkowski content $L_0(G)$ of a body $G\subset{\mathbb{R}}^d$ represents the boundary length (for $d=2$) or the surface area (for $d=3$) of $G$. A method for estimating $L_0(G)$ 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, $L_1$-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. | |
| dc.description | Published at http://dx.doi.org/10.1214/009053606000001532 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0708.2180 | |
| dc.identifier | http://arxiv.org/abs/0708.2180 | |
| dc.identifier | Annals of Statistics 2007, Vol. 35, No. 3, 1031-1051 | |
| dc.identifier | doi:10.1214/009053606000001532 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136405 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G07 (Primary) 62G20 (Secondary) | |
| dc.title | A nonparametric approach to the estimation of lengths and surface areas | |
| dc.type | text |