Author:
Armendáriz Inés,Cuevas Antonio,Fraiman Ricardo
Abstract
We study a nonparametric method for estimating the boundary measure of a compact body G ⊂ ℝ
d
(the boundary length when d = 2 and the surface area for d = 3) in the case when this measure agrees with the corresponding Minkowski content. The estimator we consider is closely related to the one proposed in Cuevas, Fraiman and Rodríguez-Casal (2007). Our method relies on two sets of random points, drawn inside and outside the set G, with different sampling intensities. Strong consistency and asymptotic normality are obtained under some shape hypotheses on the set G. Some applications and practical aspects are briefly discussed.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Cited by
1 articles.
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1. Estimating perimeter using graph cuts;Advances in Applied Probability;2017-11-17