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Extreme values and kernel estimates of point processes boundaries (1103.5931v1)
Published 30 Mar 2011 in stat.ME, math.ST, and stat.TH
Abstract: 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 a simulation.