Semiparametric Estimation of Cross-Covariance Functions for Multivariate Random Fields

• Activity Number: 308 - Recent Advancements in Spatial and Spatio-Temporal Modeling
• Type: Contributed
• Date/Time: Tuesday, July 30, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Ghulam Qadir* and Ying Sun
• Companies: King Abdullah University of Science and Technology (KAUST) and King Abdullah University of Science and Technology
• Keywords: Coherence; Co-kriging; Multivariate Random Fields; Cross-covariance

Abstract

The prevalence of spatially referenced multivariate data has impelled researchers 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. We propose a semiparametric approach for multivariate spatial covariance function estimation with approximately Matérn 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 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. Finally, we analyze the PM 2.5 and wind speed data over the United States, to show that our proposed method outperforms the commonly used full bivariate Matérn model and the linear model of coregionalization for spatial prediction.