Weighted composite likelihood-based tests for space-time separability of covariance functions
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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.
KeywordsFractal dimension Full symmetry Hurst effect Space-time covariance functions Space-time separability Weighted composite likelihood
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- Bevilacqua, M., Gaetan, C., Mateu, J., Porcu, E.: Estimating space and space-time covariance functions: a weighted composite likelihood approach. J. Am. Stat. Assoc. (2009, to appear) Google Scholar
- Crujeiras, R.M., Fernández-Casal, R., González-Manteiga, W.: Goodness-of-fit tests for spatial spectral density. Technical report 07-01, Departamento de Estadística e Investigación Operativa, Universidade de Santiago de Compostela (2008) Google Scholar
- Efron, B.: The Jackknife, the Bootstrap and Other Resampling Plans. SIAM, Philadelphia (1982) Google Scholar
- Gneiting, T., Genton, M.G., Guttorp, P.: Geostatistical space-time models, stationarity, separability and full symmetry. In: Finkenstadt, B., Held, L., Isham, V. (eds.) Statistical Methods for Spatio-Temporal Systems, pp. 151–175. Chapman & Hall/CRC, Boca Raton (2007) Google Scholar
- Hartigan, J.A.: A failure of likelihood asymptotic for normal mixtures. In: LeCam, L., Olshen, R.A. (eds.) Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer, vol. II, pp. 807–810. Wadsworth and Brooks, Belmont (1985) Google Scholar
- Porcu, E., Mateu, J., Christakos, G.: Quasi-arithmetic means of covariance functions with potential applications to space-time data. J. Multivar. Anal. (2009, to appear). doi: 10.1016/j.jmva.2009.02.013
- Scaccia, L., Martin, R.J.: Testing for simplification in spatial models. In: COMPSTAT 2002, pp. 581–586. Physica, Heidelberg (2002) Google Scholar