Covariance matrix functions of isotropic vector random fields
Wang, Renxiang Du, Juan Ma, Chunsheng
Wang, Renxiang
Du, Juan
Ma, Chunsheng
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2014-05-15
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Article
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Covariance matrix function,Cross covariance,Direct covariance,Elliptically contoured random field,Gaussian random field,Spectral density matrix function,Spherically invariant random field,Stationary
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Wang, Renxiang; Du, Juan; Ma, Chunsheng. 2014. Covariance matrix functions of isotropic vector random fields. Communications in Statistics - Theory and Methods, SI: Advances in Probability and Statistics, vol. 43:no. 10-12:ppg. 2081-2093
Abstract
An isotropic scalar or vector random field is a second-order random field in (d > 2), whose covariance function or direct/cross covariance functions are isotropic. While isotropic scalar random fields have been well developed and widely used in various sciences and industries, the theory of isotropic vector random fields needs to be investigated for applications. The objective of this article is to study properties of covariance matrix functions associated with vector random fields in which are stationary, isotropic, and mean square continuous, and derives the characterizations of the covariance matrix function of the Gaussian or second-order elliptically contoured vector random field in . In particular, integral or spectral representations for isotropic and continuous covariance matrix functions are derived.
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Taylor & Francis Group
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Communications in Statistics - Theory and Methods
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0361-0926