A Valid Matérn Class of Cross-Covariance Functions for Multivariate Random Fields With Any Number of Components

Type
Article

Authors
Apanasovich, Tatiyana V.
Genton, Marc G.
Sun, Ying

KAUST Grant Number
KUS-C1-016-04

Date
2012-03

Abstract
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. 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 Matérnmodel 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 Matérn model is valid and yields better predictive scores compared with a parsimonious model with common scale parameters. © 2012 American Statistical Association.

Citation
Apanasovich TV, Genton MG, Sun Y (2012) A Valid Matérn Class of Cross-Covariance Functions for Multivariate Random Fields With Any Number of Components. Journal of the American Statistical Association 107: 180–193. Available: http://dx.doi.org/10.1080/01621459.2011.643197.

Acknowledgements
This publication is based in part on work supported by award no. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST) and by NSF grants DMS-1007504 and DMS-0707106. The authors thank the editor, two referees, and Tilmann Gneiting for their helpful comments and suggestions.

Publisher
Informa UK Limited

Journal
Journal of the American Statistical Association

DOI
10.1080/01621459.2011.643197

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