Geodesic
Extreme values and kernel estimates of point processes boundaries
ESAIM: Probability and Statistics, Tome 8 (2004), pp. 150-168

Voir la notice de l'article provenant de la source Numdam

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.

DOI : 10.1051/ps:2004008
Classification : 60G70, 62G05, 62G20, 62M30
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 = {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

Cité par Sources :