Nonparametric estimation of boundary measures and related functionals: asymptotic results
2009 ◽
Vol 41
(2)
◽
pp. 311-322
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Keyword(s):
We study a nonparametric method for estimating the boundary measure of a compact body G ⊂ ℝd (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.
2009 ◽
Vol 41
(02)
◽
pp. 311-322
◽
Yule–Walker type estimators in periodic bilinear models: strong consistency and asymptotic normality
2008 ◽
Vol 19
(1)
◽
pp. 1-30
◽
2010 ◽
Vol 80
(19-20)
◽
pp. 1532-1542
◽
1991 ◽
pp. 443-462
◽
1991 ◽
Vol 12
(2)
◽
pp. 95-104
◽