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Extreme values and kernel estimates of point processes boundaries

Published online by Cambridge University Press:  15 September 2004

Stéphane Girard  and
Pierre Jacob
Stéphane Girard
Affiliation:
SMS/LMC, Université Grenoble 1, BP 53, 38041 Grenoble Cedex 9, France; Stephane.Girard@imag.fr.
Pierre Jacob
Affiliation:
EPS/I3M, Université Montpellier 2, place Eugène Bataillon, 34095 Montpellier Cedex 5, France; jacob@math.univ-montp2.fr.
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Abstract

We present a method for estimating the edge of a two-dimensional bounded set, given a finite random set of points drawn from the interior. The estimator is based both on a Parzen-Rosenblatt kernel and extreme values of point processes. We give conditions for various kinds of convergence and asymptotic normality. We propose a method of reducing the negative bias and edge effects, illustrated by some simulations.

Keywords

Kernel estimatesextreme valuesPoisson processshape estimation.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 8 , August 2004 , pp. 150 - 168
Copyright
© EDP Sciences, SMAI, 2004

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