Central limit theorems for smoothed extreme value estimates of Poisson point processes boundaries

TL;DR

This paper establishes central limit theorems for smoothed boundary estimates of Poisson point processes, enabling Gaussian-based confidence intervals and providing new examples in both unidimensional and multidimensional settings.

Contribution

It introduces sufficient conditions for CLTs of smoothed boundary estimates, combining bias correction and smoothing techniques for Poisson processes.

Findings

Smoothing yields Gaussian asymptotic distributions.

Provides pointwise confidence intervals for boundary estimates.

Includes new unidimensional and multidimensional examples.

Abstract

In this paper, we give sufficient conditions to establish central limit theorems for boundary estimates of Poisson point processes. The considered estimates are obtained by smoothing some bias corrected extreme values of the point process. We show how the smoothing leads Gaussian asymptotic distributions and therefore pointwise confidence intervals. Some new unidimensional and multidimensional examples are provided.