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1 results

Extreme values and kernel estimates of point processes boundaries
Stéphane Girard, Pierre Jacob
Journal:

ESAIM: Probability and Statistics / Volume 8 / August 2004

Published online by Cambridge University Press:

15 September 2004, pp. 150-168

Print publication:

August 2004
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We present a method for estimating the edge of a two-dimensionalbounded 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 conditionsfor various kinds of convergence and asymptotic normality.We propose a method of reducing the negative bias and edge effects,illustrated by some simulations.