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Classes of compactly supported covariance functions for multivariate random fields
- Daley, Daryl J., Porcu, Emilio, Bevilacqua, Moreno
- Stochastic environmental research and risk assessment 2015 v.29 no.4 pp. 1249-1263
- covariance, data collection, models, temperature
- The paper combines simple general methodologies to obtain new classes of matrix-valued covariance functions that have two important properties: (i) the domains of the compact support of the several components of the matrix-valued functions can vary between components; and (ii) the overall differentiability at the origin can also vary. These models exploit a class of functions called here the Wendland–Gneiting class; their use is illustrated via both a simulation study and an application to a North American bivariate dataset of precipitation and temperature. Because for this dataset, as for others, the empirical covariances exhibit a hole effect, the turning bands operator is extended to matrix-valued covariance functions so as to obtain matrix-valued covariance models with negative covariances.