Premium
Isotropic spectral additive models of the covariogram
Author(s) -
Powojowski Miro R.
Publication year - 2008
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2008.00653.x
Subject(s) - covariance , covariance function , mathematics , estimator , rational quadratic covariance function , spectral density , spectral representation , estimation of covariance matrices , isotropy , matérn covariance function , spectral density estimation , function (biology) , covariance intersection , mathematical analysis , statistics , fourier transform , physics , quantum mechanics , evolutionary biology , biology , quantum electrodynamics
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.