On minimum contrast method for multivariate spatial point processes

TL;DR

This paper introduces a new minimum contrast method for estimating parameters in multivariate spatial point processes, offering computational efficiency and asymptotic properties, demonstrated through simulation studies.

Contribution

The paper develops a novel MC estimation technique specifically for multivariate spatial point processes, extending its application beyond univariate models.

Findings

The proposed MC estimator is asymptotically normal.

Simulation studies show competitive performance with likelihood-based methods.

Method is computationally efficient for complex multivariate models.

Abstract

Compared to widely used likelihood-based approaches, the minimum contrast (MC) method offers a computationally efficient method for estimation and inference of spatial point processes. These relative gains in computing time become more pronounced when analyzing complicated multivariate point process models. Despite this, there has been little exploration of the MC method for multivariate spatial point processes. Therefore, this article introduces a new MC method for parametric multivariate spatial point processes. A contrast function is computed based on the trace of the power of the difference between the conjectured $K$-function matrix and its nonparametric unbiased edge-corrected estimator. Under standard assumptions, we derive the asymptotic normality of our MC estimator. The performance of the proposed method is demonstrated through simulation studies of bivariate log-Gaussian Cox processes and five-variate product-shot-noise Cox processes.