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 estimates, extreme values, Poisson process, shape estimation
@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 = {https://www.numdam.org/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 - https://www.numdam.org/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 https://www.numdam.org/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. https://www.numdam.org/articles/10.1051/ps:2004008/
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