| Issue |
ESAIM: PS
Volume 8, August 2004
|
|
|---|---|---|
| Page(s) | 150 - 168 | |
| DOI | https://doi.org/10.1051/ps:2004008 | |
| Published online | 15 September 2004 | |
Extreme values and kernel estimates of point processes boundaries
1
SMS/LMC, Université Grenoble 1,
BP 53, 38041 Grenoble Cedex 9, France;
Stephane.Girard@imag.fr.
2
EPS/I3M, Université Montpellier 2,
place Eugène Bataillon, 34095 Montpellier Cedex 5, France; jacob@math.univ-montp2.fr.
Received:
26
June
2003
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
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