Cross-Covariance Functions for Multivariate Random Fields Based on Latent Dimensions

• Activity Number: 118
• Type: Topic Contributed
• Date/Time: Monday, August 2, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Marc Genton*+ and Tatiyana Apanasovich
• Companies: Texas A&M University and Thomas Jefferson University
• Keywords: Asymmetry ; Linear model of coregionalization ; Nonseparability ; Positive definiteness ; Space and Time ; Stationarity

Abstract

The problem of constructing valid parametric cross-covariance functions is challenging. We propose a simple methodology, based on latent dimensions and existing covariance models for univariate random fields, to develop flexible, interpretable, and computationally feasible classes of cross-covariance functions in closed form. We focus on spatio-temporal cross-covariance functions that can be nonseparable, asymmetric, and can have different covariance structures, for instance different smoothness parameters, in each component. We discuss estimation of these models and perform a small simulation study to demonstrate our approach. We illustrate our methodology on a trivariate spatio-temporal pollution dataset from California and demonstrate that our cross-covariance performs better than other competing models.