Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes

TL;DR

This paper introduces a local estimation method for spatio-temporal log-Gaussian Cox processes using LISTA functions, enabling the modeling of space and time-varying parameters with improved flexibility.

Contribution

It develops a novel local minimum contrast estimation approach incorporating LISTA functions for flexible spatio-temporal modeling of Cox processes.

Findings

Simulation studies demonstrate the method's effectiveness.

Application to seismic data shows practical utility.

Flexible in both separable and non-separable models.

Abstract

We propose a local version of spatio-temporal log-Gaussian Cox processes using Local Indicators of Spatio-Temporal Association (LISTA) functions into the minimum contrast procedure to obtain space as well as time-varying parameters. We resort to the joint minimum contrast fitting method to estimate the set of second-order parameters. This approach has the advantage of being suitable in both separable and non-separable parametric specifications of the correlation function of the underlying Gaussian Random Field. We present simulation studies to assess the performance of the proposed fitting procedure, and show an application to seismic spatio-temporal point pattern data.