Projection estimates of point processes boundaries

TL;DR

This paper introduces a new method for estimating the boundary of a 2D set from interior point samples, combining projection techniques and extreme point analysis, with theoretical convergence results and bias reduction strategies.

Contribution

It presents a novel boundary estimation approach using projections on C^1 bases and extreme points, with conditions for convergence and asymptotic normality, and includes bias reduction methods.

Findings

Convergence conditions based on Dirichlet's kernel

Asymptotic normality of the estimator

Effective bias reduction demonstrated by simulation

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 projections on C^1 bases and on extreme points of the point process. We give conditions on the Dirichlet's kernel associated to the C^1 bases for various kinds of convergence and asymptotic normality. We propose a method for reducing the negative bias and illustrate it by a simulation.