A Valid MatÃ©rn Class of Cross-Covariance Functions for Multivariate Random Fields With Any Number of Components
Tatiyana V. Apanasovich,
Marc G. Genton and
Journal of the American Statistical Association, 2012, vol. 107, issue 497, 180-193
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 MatÃ©rn 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. We discuss practical implementations, including reparameterizations to reflect the conditions on the parameter space and an iterative algorithm to increase the computational efficiency. 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 MatÃ©rn model is illustrated on two meteorological datasets: temperature/pressure over the Pacific Northwest (bivariate) and wind/temperature/pressure in Oklahoma (trivariate). In the latter case, our flexible trivariate MatÃ©rn model is valid and yields better predictive scores compared with a parsimonious model with common scale parameters.
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