Bootstrapping kernel intensity estimation for nonhomogeneous point processes depending on spatial covariates

TL;DR

This paper develops a theoretically grounded, consistent kernel intensity estimator for nonhomogeneous spatial point processes that incorporate covariates, along with a bootstrap method and data-driven bandwidth selectors, validated through simulations and real wildfire data.

Contribution

It introduces a new consistent kernel intensity estimator using covariates, along with a bootstrap procedure and bandwidth selectors, advancing the analysis of spatial point processes.

Findings

The proposed estimator is consistent and effective in finite samples.

The bootstrap method provides reliable bandwidth selection.

Application to wildfire data demonstrates practical utility.

Abstract

In the spatial point process context, kernel intensity estimation has been mainly restricted to exploratory analysis due to its lack of consistency. Different methods have been analysed to overcome this problem, and the inclusion of covariates resulted to be one possible solution. In this paper we focus on de\-fi\-ning a theoretical framework to derive a consistent kernel intensity estimator using covariates, as well as a consistent smooth bootstrap procedure. We define two new data-driven bandwidth selectors specifically designed for our estimator: a rule-of-thumb and a plug-in bandwidth based on our consistent bootstrap method. A simulation study is accomplished to understand the performance of our proposals in finite samples. Finally, we describe an application to a real data set consisting of the wildfires in Canada during June 2015, using meteorological information as covariates.