Nonstationary modeling for multivariate spatial processes

William Kleiber and Douglas Nychka

Journal of Multivariate Analysis, 2012, vol. 112, issue C, 76-91

Abstract: We derive a class of matrix valued covariance functions where the direct and cross-covariance functions are Matérn. The parameters of the Matérn 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.

Keywords: Cross-covariance; Kernel smoother; Local stationarity; Matérn; Multivariate; Nonstationary; Spatial Gaussian process (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (11)

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DOI: 10.1016/j.jmva.2012.05.011

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