Nonstationary modeling for multivariate spatial processes

Authors:
William Kleiber;Douglas Nychka
Affiliations:
-;-
Venue:
Journal of Multivariate Analysis
Year:
2012

Citing 5
Cited 0

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Quasi-arithmetic means of covariance functions with potential applications to space-time data

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Characterization theorems for some classes of covariance functions associated to vector valued random fields

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An approach to modeling asymmetric multivariate spatial covariance structures

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Abstract

We derive a class of matrix valued covariance functions where the direct and cross-covariance functions are Matern. The parameters of the Matern class are allowed to vary with location, yielding local variances, local ranges, local geometric anisotropies and local smoothnesses. We discuss inclusion of a nonconstant cross-correlation coefficient and a valid approximation. Estimation utilizes kernel smoothed empirical covariance matrices and a locally weighted minimum Frobenius distance that yields local parameter estimates at any location. We derive the asymptotic mean squared error of our kernel smoother and discuss the case when multiple field realizations are available. Finally, the model is illustrated on two datasets, one a synthetic bivariate one-dimensional spatial process, and the second a set of temperature and precipitation model output from a regional climate model.