Extreme values and kernel estimates of point processes boundaries
Stéphane Girard1 and Pierre Jacob2
SMS/LMC, Université Grenoble 1,
BP 53, 38041 Grenoble Cedex 9, France;
2 EPS/I3M, Université Montpellier 2, place Eugène Bataillon, 34095 Montpellier Cedex 5, France; firstname.lastname@example.org.
Revised: 26 March 2004
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.
Mathematics Subject Classification: 60G70 / 62G05 / 62G20 / 62M30
Key words: Kernel estimates / extreme values / Poisson process / shape estimation.
© EDP Sciences, SMAI, 2004