Bandwidth selection for kernel estimators of the spatial intensity function

TL;DR

This paper reviews existing methods and introduces a new non-parametric approach for selecting bandwidths in kernel estimators of spatial point process intensity functions, enhancing flexibility and applicability.

Contribution

It proposes a novel bandwidth selection method based on the Campbell formula, which is fully non-parametric and model-agnostic.

Findings

The new method performs well across various spatial point process models.

It does not require prior knowledge of product densities.

The approach is versatile and applicable to different types of spatial data.

Abstract

We discuss and compare various approaches to the problem of bandwidth selection for kernel estimators of intensity functions of spatial point processes. We also propose a new method based on the Campbell formula applied to the reciprocal intensity function. The new method is fully non-parametric, does not require knowledge of the product densities, and is not restricted to a specific class of point process models.