Semiparametric Estimation of Cross-covariance Functions for Multivariate Random Fields

TL;DR

This paper introduces a semiparametric method for estimating multivariate spatial covariance functions that offers greater flexibility and improved spatial prediction accuracy over traditional models, especially in environmental data analysis.

Contribution

It proposes a novel spectral-based semiparametric approach with B-spline coherence functions for flexible cross-covariance modeling in multivariate spatial data.

Findings

Method accurately estimates coherence functions in simulations.

Outperforms traditional models in spatial prediction of environmental data.

Demonstrates flexibility and improved fit for real-world PM2.5 and wind speed data.

Abstract

The prevalence of spatially referenced multivariate data has impelled researchers to develop a procedure for the joint modeling of multiple spatial processes. This ordinarily involves modeling marginal and cross-process dependence for any arbitrary pair of locations using a multivariate spatial covariance function. However, building a flexible multivariate spatial covariance function that is nonnegative definite is challenging. Here, we propose a semiparametric approach for multivariate spatial covariance function estimation with approximate Mat\'ern marginals and highly flexible cross-covariance functions via their spectral representations. The flexibility in our cross-covariance function arises due to B-spline based specification of the underlying coherence functions, which in turn allows us to capture non-trivial cross-spectral features. We then develop a likelihood-based estimation procedure and perform multiple simulation studies to demonstrate the performance of our method, especially on the coherence function estimation. Finally, we analyze particulate matter concentrations ($\text{PM}_{2.5}$) and wind speed data over the North-Eastern region of the United States, where we illustrate that our proposed method outperforms the commonly used full bivariate Mat\'ern model and the linear model of coregionalization for spatial prediction.