Article
Spherically Invariant Vector Random Fields in Space and Time
IEEE Transactions on Signal Processing (Impact Factor: 2.81). 01/2012; DOI: 10.1109/TSP.2011.2166391
Source: IEEE Xplore

Article: MittagLeffler vector random fields with MittagLeffler direct and cross covariance functions
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ABSTRACT: In terms of the twoparameter MittagLeffler function with specified parameters, this paper introduces the MittagLeffler vector random field through its finitedimensional characteristic functions, which is essentially an elliptically contoured one and reduces to a Gaussian one when the two parameters of the MittagLeffler function equal 1. Having secondorder moments, a MittagLeffler vector random field is characterized by its mean function and its covariance matrix function, just like a Gaussian one. In particular, we construct direct and cross covariances of MittagLeffler type for such vector random fields.Annals of the Institute of Statistical Mathematics 01/2013; · 0.74 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: This paper presents the characterization of the covariance matrix function of a Gaussian or secondorder elliptically contoured vector random field on the sphere which is stationary, isotropic, and mean square continuous. This characterization involves an infinite sum of the products of positive definite matrices and Gegenbauer’s polynomials, and may not be available for other nonGaussian vector random fields on spheres such as a χ 2 or logGaussian vector random field. We also offer two simple but efficient constructing approaches, and derive some parametric covariance matrix structures on spheres.Mathematical geosciences 44(6). · 1.44 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: This paper is concerned with vector random fields on spheres with secondorder increments, which are intrinsically stationary and mean square continuous and have isotropic variogram matrix functions. A characterization of the continuous and isotropic variogram matrix function on a sphere is derived, in terms of an infinite sum of the products of positive definite matrices and ultraspherical polynomials. It is valid for Gaussian or elliptically contoured vector random fields, but may not be valid for other nonGaussian vector random fields on spheres such as a χ 2, logGaussian, or skewGaussian vector random field. Some parametric variogram matrix models are derived on spheres via different constructional approaches. A simulation study is conducted to illustrate the implementation of the proposed model in estimation and cokriging, whose performance is compared with that using the linear model of coregionalization.Mathematical geosciences 01/2013; 45(3). · 1.44 Impact Factor
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