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Testing the covariance structure of multivariate random fields
Department of Statistics, Purdue University, West Lafayette, Indiana 47907, U.S.A. boli{at}purdue.edu
Department of Statistics, Texas A&M University, College Station, Texas 77843, U.S.A. genton{at}stat.tamu.edu
Department of Statistics, Texas A&M University, College Station, Texas 77843, U.S.A. sherman{at}stat.tamu.edu
Received for publication 1 August 2007. Revision received 1 May 2008.
There is an increasing wealth of multivariate spatial and multivariate spatio-temporal data appearing. For such data, an important part of model building is an assessment of the properties of the underlying covariance function describing variable, spatial and temporal correlations. In this paper, we propose a methodology to evaluate the appropriateness of several types of common assumptions on multivariate covariance functions in the spatio-temporal context. The methodology is based on the asymptotic joint normality of the sample space-time cross-covariance estimators. Specifically, we address the assumptions of symmetry, separability and linear models of coregionalization. We conduct simulation experiments to evaluate the sizes and powers of our tests and illustrate our methodology on a trivariate spatio-temporal dataset of pollutants over California.
Key Words: Covariance • Linear model of coregionalization • Separability • Space and time • Symmetry
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