Extreme values and kernel estimates of point processes boundaries
Methodology
2011-03-31 v1 Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.1103.5931,
title = {Extreme values and kernel estimates of point processes boundaries},
author = {Stéphane Girard and Pierre Jacob},
journal= {arXiv preprint arXiv:1103.5931},
year = {2011}
}