Non-parametric adaptive bandwidth selection for kernel estimators of spatial intensity functions

TL;DR

This paper introduces a new non-parametric, adaptive bandwidth selection method for kernel estimators of spatial intensity functions, improving estimation accuracy for spatial point processes like earthquake data.

Contribution

It presents a novel two-step adaptive bandwidth selection approach based on the Campbell-Mecke formula and Abramson's law, outperforming existing global methods.

Findings

The method performs well in simulations compared to existing selectors.

Applied to earthquake data, it effectively estimates spatial intensity.

Demonstrates improved local estimation accuracy.

Abstract

We propose a new fully non-parametric two-step adaptive bandwidth selection method for kernel estimators of spatial point process intensity functions based on the Campbell-Mecke formula and Abramson's square root law. We present a simulation study to assess its performance relative to the Cronie-Van Lieshout global bandwidth selector and apply the technique to data on induced earthquakes in theGroningen gas field.