Spatially varying cross-correlation coefficients in the presence of nugget effects
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Spatio-Temporal Statistics and Data Analysis Group
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AbstractWe derive sufficient conditions for the cross-correlation coefficient of a multivariate spatial process to vary with location when the spatial model is augmented with nugget effects. The derived class is valid for any choice of covariance functions, and yields substantial flexibility between multiple processes. The key is to identify the cross-correlation coefficient matrix with a contraction matrix, which can be either diagonal, implying a parsimonious formulation, or a fully general contraction matrix, yielding greater flexibility but added model complexity. We illustrate the approach with a bivariate minimum and maximum temperature dataset in Colorado, allowing the two variables to be positively correlated at low elevations and nearly independent at high elevations, while still yielding a positive definite covariance matrix. © 2012 Biometrika Trust.
SponsorsThis research was partially supported by an award made by the King Abdullah University of Science and Technology and by the National Science Foundation.
PublisherOxford University Press (OUP)