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A valid Matérn class of cross-covariance functions for multivariate random fields with any number of components. (English) Zbl 1261.62087

Summary: 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 Matérn class [B. Matérn, Spatial variation. 2nd ed. Berlin: Springer (1986; Zbl 0608.62122)]. Unlike previous attempts, our model indeed allows for various smoothnesses and rates of correlation decay for any number of vector components. We present 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 Matérn model is illustrated on two meteorological data sets: temperature/pressure over the Pacific Northwest (bivariate) and wind/temperature/pressure in Oklahoma (trivariate). In the latter case, our flexible trivariate Matérn model is valid and yields better predictive scores compared with a parsimonious model with common scale parameters.

MSC:

62M40 Random fields; image analysis
62H12 Estimation in multivariate analysis
65C05 Monte Carlo methods
62P12 Applications of statistics to environmental and related topics

Citations:

Zbl 0608.62122
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References:

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