Extreme values and kernel estimates of point processes boundaries

TL;DR

This paper introduces a novel method combining kernel estimation and extreme value theory to accurately estimate the boundary of a 2D set from interior points, with proven convergence properties.

Contribution

It proposes a new boundary estimation technique using kernel and extreme value methods, with bias reduction and asymptotic analysis.

Findings

Estimator converges under specified conditions

Method reduces bias and edge effects

Simulation demonstrates effectiveness

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.