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Flexible multivariate covariance models for spatial data are on demand. This paper addresses the problem of parametric constraints for positive semidefiniteness of the multivariate Mat{e}rn model. Much attention has been given to the bivariate case, while highly multivariate cases have been explored to a limited extent only. The existing conditions often imply severe restrictions on the upper bounds for the collocated correlation coefficients, which makes the multivariate Mat{e}rn model appealing for the case of weak spatial cross-dependence only. We provide a collection of validity conditions for the multivariate Mat{e}rn covariance model that allows for more flexible parameterizations than those currently available. We also prove that, in several cases, we can attain much higher upper bounds for the collocated correlation coefficients in comparison with our competitors. We conclude with a simple illustration on a trivariate geochemical dataset and show that our enlarged parametric space allows for better fitting performance with respect to our competitors.
The assumption of separability of the covariance operator for a random image or hypersurface can be of substantial use in applications, especially in situations where the accurate estimation of the full covariance structure is unfeasible, either for
We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we introduce element-
Monitoring several correlated quality characteristics of a process is common in modern manufacturing and service industries. Although a lot of attention has been paid to monitoring the multivariate process mean, not many control charts are available
In this paper, a new mixture family of multivariate normal distributions, formed by mixing multivariate normal distribution and skewed distribution, is constructed. Some properties of this family, such as characteristic function, moment generating fu
Multivariate space-time data are increasingly available in various scientific disciplines. When analyzing these data, one of the key issues is to describe the multivariate space-time dependencies. Under the Gaussian framework, one needs to propose re