A nonparametric approach to the estimation of lengths and surface areas
Entity
UAM. Departamento de MatemáticasPublisher
Annals of StatisticsDate
2007-07-01Citation
10.1214/009053606000001532
The Annals of Statistics 35.3 (2007): 1031-1051
ISSN
0090-5364 (print)DOI
10.1214/009053606000001532Funded by
Supported in part by Spanish Grant MTM2004-00098, MTM2005-00820 and PGIDIT06PXIB207009PRProject
Gobierno de España. MTM2004-00098; Gobierno de España. MTM2005-00820; Gobierno de España. PGIDIT06PXIB207009PREditor's Version
http://dx.doi.org/10.1214/009053606000001532Subjects
Length estimation; Minkowski content; Nonparametric set estimation; Statistical image analysis; MatemáticasRights
© Institute of Mathematical Statistics, 2007Abstract
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
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Google Scholar:Cuevas González, Antonio
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Fraiman, Ricardo
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Rodríguez-Casal, Alberto
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