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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.
@article{PS_2004__8__150_0,
author = {Girard, St\'ephane and Jacob, Pierre},
title = {Extreme values and kernel estimates of point processes boundaries},
journal = {ESAIM: Probability and Statistics},
pages = {150--168},
publisher = {EDP-Sciences},
volume = {8},
year = {2004},
doi = {10.1051/ps:2004008},
mrnumber = {2085612},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2004008/}
}
TY - JOUR AU - Girard, Stéphane AU - Jacob, Pierre TI - Extreme values and kernel estimates of point processes boundaries JO - ESAIM: Probability and Statistics PY - 2004 SP - 150 EP - 168 VL - 8 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ps:2004008/ DO - 10.1051/ps:2004008 LA - en ID - PS_2004__8__150_0 ER -
%0 Journal Article %A Girard, Stéphane %A Jacob, Pierre %T Extreme values and kernel estimates of point processes boundaries %J ESAIM: Probability and Statistics %D 2004 %P 150-168 %V 8 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ps:2004008/ %R 10.1051/ps:2004008 %G en %F PS_2004__8__150_0
Girard, Stéphane; Jacob, Pierre. Extreme values and kernel estimates of point processes boundaries. ESAIM: Probability and Statistics, Tome 8 (2004), pp. 150-168. doi: 10.1051/ps:2004008
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