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

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 
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     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},
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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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