Smoothed extreme value estimators of non-uniform point processes boundaries with application to star-shaped supports estimation

TL;DR

This paper introduces a new smoothing-based method for estimating the boundary of a bounded set in R^d from interior points, with a focus on star-shaped supports, improving boundary estimation accuracy.

Contribution

It proposes a novel transformation and smoothing technique for extreme value estimators tailored to non-uniform point processes, enhancing boundary estimation methods.

Findings

Effective boundary estimation for star-shaped supports

Improved accuracy over existing methods

Applicable to non-uniform point processes

Abstract

We address the problem of estimating the edge of a bounded set in R^d given a random set of points drawn from the interior. Our method is based on a transformation of estimators dedicated to uniform point processes and obtained by smoothing some of its bias corrected extreme points. An application to the estimation of star-shaped supports is presented.