Factor Copula Models for Replicated Spatial Data

TL;DR

This paper introduces a new factor copula model for replicated spatial data that captures tail dependence and asymmetry, offering flexible dependence modeling and efficient likelihood estimation.

Contribution

The paper presents a novel factor copula model for spatial data that allows for tail dependence and asymmetry, with closed-form density for certain factors and efficient estimation methods.

Findings

Model captures a wide range of dependence structures.

Likelihood estimation remains fast for large datasets.

Outperforms some geostatistical models in temperature data application.

Abstract

We propose a new copula model that can be used with replicated spatial data. Unlike the multivariate normal copula, the proposed copula is based on the assumption that a common factor exists and affects the joint dependence of all measurements of the process. Moreover, the proposed copula can model tail dependence and tail asymmetry. The model is parameterized in terms of a covariance function that may be chosen from the many models proposed in the literature, such as the Matern model. For some choice of common factors, the joint copula density is given in closed form and therefore likelihood estimation is very fast. In the general case, one-dimensional numerical integration is needed to calculate the likelihood, but estimation is still reasonably fast even with large data sets. We use simulation studies to show the wide range of dependence structures that can be generated by the proposed model with different choices of common factors. We apply the proposed model to spatial temperature data and compare its performance with some popular geostatistics models.