A multivariate spatial modeling approach using semi-parametric covariance functions
The major challenge of designing a multivariate spatial model comes from the specification of the multivariate covariogram, which must be positive definite. Most current approaches to multivariate spatial modeling take a parametric approach which chooses both the direct-covariograms and the cross-covariograms from some parametric family and that places restrictions on the choice of the form and the parameters in the cross-covariogram. In this work, we propose a semi-parametric approach which builds the cross-covariogram upon the direct-covariograms from the marginal models. Our approach still uses parametric covariograms for the marginal models for the multivariate process but includes a non-parametric cross-covariogram. ^ The estimation of the non-parametric cross-covariogram poses a combinatorial optimization problem. We propose two algorithms as the solutions: a progressive search algorithm and the simulated annealing. The performance of the semi-parametric modeling approach has been tested through simulations and analysis of real data. The results show that this approach provides better predictive performance than some existing multivariate spatial models.^
Hao Zhang, Purdue University.