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Isotropic spectral additive models of the covariogram

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  • Miro R. Powojowski

Abstract

Summary. A class of additive covariance models of an isotropic random process is proposed, motivated by the spectral representation of the covariance function. Model parameters are estimated by using a special case of the minimum norm quadratic estimation estimator, whose asymptotic moments have convenient expressions in terms of spectral densities. Fitting a model in this class is equivalent to fitting an additive model of the spectral density. The class of spectral additive models proposed is dense in the set of summable covariance functions having a spectral density, allowing approximately unbiased estimation of an arbitrary covariance function and its spectral density. Theoretical results are supported by numerical comparison with commonly used models. A procedure to assist model selection is proposed. The techniques are illustrated with an application to contaminant data.

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  • Miro R. Powojowski, 2008. "Isotropic spectral additive models of the covariogram," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 739-753, September.
    • Handle: RePEc:bla:jorssb:v:70:y:2008:i:4:p:739-753
    DOI: 10.1111/j.1467-9868.2008.00653.x
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    1. Shapiro, A. & Botha, J. D., 1991. "Variogram fitting with a general class of conditionally nonnegative definite functions," Computational Statistics & Data Analysis, Elsevier, vol. 11(1), pages 87-96, January.
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