We introduce a valid parametric family of cross-covariance functions for multivariate spatial random fields where each component has a covariance function from a well-celebrated Matern class. Unlike previous attempts, our model indeed allows for various smoothnesses and rates of correlation decay for any number of vector components. We present the conditions on the parameter space that result in valid models with varying degrees of complexity. Practical implementations, including reparametrizations to reflect the conditions on the parameter space and an iterative algorithm to increase the computational efficiency, are discussed. We perform various Monte Carlo simulation experiments to explore the performances of our approach in terms of estimation and cokriging. The application of the proposed multivariate Matern model is illustrated on two meteorological datasets: Temperature/Pressure over the Pacific Northwest (bivariate) and Wind/Temperature/Pressure in Oklahoma (trivariate).
Keywords: Cokriging; Smoothness; Multivariate; Spatial
Biography: Marc G. Genton completed his Ph.D. in Statistics at the Swiss Federal Institute of Technology (EPFL), Lausanne, in 1996. He is a Professor of Statistics at Texas A&M University, the Director of the Program in Spatial Statistics (PSS), and a Deputy Director for the Institute of Applied Mathematics and Computational Science (IAMCS). He is a Fellow of the American Statistical Association, of the Institute of Mathematical Statistics, and elected member of the International Statistical Institute. In 2010, he received the El-Shaarawi award for excellence from the International Environmetrics Society and the Distinguished Achievement award from the Section on Statistics and the Environment of the American Statistical Association. His research interests include spatial and spatio-temporal statistics with applications in environmental and climate science; wind power forecasting; times series; robustness; multivariate analysis and data mining; and skewed multivariate non-gaussian distributions.