A multivariate spatial modeling approach using semi-parametric covariance functions

Yong Wang, Purdue University

Abstract

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.

Degree

Ph.D.

Advisors

Zhang, Purdue University.

Subject Area

Statistics

COinS