Is Bootstrap Really Helpful in Point Process Statistics?

TL;DR

This paper critically examines the application of bootstrap methods in point process statistics, demonstrating that some uses are dubious, unnecessary, or less effective than simpler, non-simulation alternatives.

Contribution

It challenges existing bootstrap applications in point process analysis, showing they can be replaced by simpler, more accurate methods for variance estimation and confidence regions.

Findings

Bootstrap methods can lead to unreliable variance estimates.

Simple non-simulation methods suffice for confidence regions.

Some bootstrap applications in point process statistics are unnecessary.

Abstract

There are some papers which describe the use of bootstrap techniques in point process statistics. The aim of the present paper is to show that the form in which bootstrap is used there is dubious. In case of variance estimation of pair correlation function estimators the used bootstrap techniques lead to results which can be obtained simpler without simulation; furthermore, they differ from the desired results. The problem to obtain confidence regions for the intensity function of inhomogeneous Poisson processes can be easily solved without bootstrap techniques.