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

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

Research output: Contribution to journalArticlepeer-review

56 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)180-193
Number of pages14
JournalJournal of the American Statistical Association
Volume107
Issue number497
DOIs
StatePublished - Mar 2012
Externally publishedYes

Fingerprint Dive into the research topics of 'A Valid Matérn Class of Cross-Covariance Functions for Multivariate Random Fields With Any Number of Components'. Together they form a unique fingerprint.

Cite this