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Variogram matrix functions for vector random fields with second-order increments
Du, Juan Ma, Chunsheng
Du, Juan
Ma, Chunsheng
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2012-05
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Article
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Keywords
Bernstein function,Conditionally negative definite matrix,Covariance matrix,Elliptically contoured random field,Gaussian random field,Schoenberg-Lévy kernel,Variogram matrix
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Citation
Du, Juan and Chunsheng Ma. 2012. "Variogram Matrix Functions for Vector Random Fields with Second-Order Increments". Mathematical Geosciences. 44 (4): 411-425.
Abstract
The variogram matrix function is an important measure for the dependence of a vector random field with second-order increments, and is a useful tool for linear predication or cokriging. This paper proposes an efficient approach to construct variogram matrix functions, based on three ingredients: a univariate variogram, a conditionally negative definite matrix, and a Bernstein function, and derives three classes of variogram matrix functions for vector elliptically contoured random fields. Moreover, various dependence structures among components can be derived through appropriate mixture procedures demonstrated in this paper. We also obtain covariance matrix functions for second-order vector random fields through the Schoenberg–Lévy kernels.
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Springer
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Mathematical Geosciences;2012, Vol. 44, No. 4
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1874-8961