Isotropic Variogram Matrix Functions on Spheres |
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Authors: | Juan Du Chunsheng Ma Yang Li |
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Institution: | 1. Department of Statistics, Kansas State University, Manhattan, KS, 66506-0802, USA 2. Department of Mathematics, Statistics, and Physics, Wichita State University, Wichita, KS, 67260-0033, USA 3. School of Economics, Wuhan University of Technology, Wuhan, Hubei, 430070, China 4. Department of Statistics, Iowa State University, Ames, IA, 50011, USA
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Abstract: | This paper is concerned with vector random fields on spheres with second-order 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 non-Gaussian vector random fields on spheres such as a χ 2, log-Gaussian, or skew-Gaussian 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. |
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