Weighted composite likelihood-based tests for space-time separability of covariance functions

Authors:
M. Bevilacqua;J. Mateu;E. Porcu;H. Zhang;A. Zini
Affiliations:
Dipartimento di Scienze Statistiche, Università di Padova, Padova, Italy;Department of Mathematics, Universitat Jaume I, Castellón, Spain;Department of Mathematics, Universitat Jaume I, Castellón, Spain;Department of Statistics, Purdue University, West Lafayette, USA 47906;Department of Quantitative Methods for Business and Economic Sciences, University of Milano Bicocca, Milan, Italy
Venue:
Statistics and Computing
Year:
2010

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Abstract

Testing for separability of space-time covariance functions is of great interest in the analysis of space-time data. In this paper we work in a parametric framework and consider the case when the parameter identifying the case of separability of the associated space-time covariance lies on the boundary of the parametric space. This situation is frequently encountered in space-time geostatistics. It is known that classical methods such as likelihood ratio test may fail in this case.We present two tests based on weighted composite likelihood estimates and the bootstrap method, and evaluate their performance through an extensive simulation study as well as an application to Irish wind speeds. The tests are performed with respect to a new class of covariance functions, which presents some desirable mathematical features and has margins of the Generalized Cauchy type. We also apply the test on a element of the Gneiting class, obtaining concordant results.