Multivariate Matérn models - A spectral approach

2449 

Contributed Abstract 

Paper 

Andrew Yarger (1), Stilian Stoev (2), Tailen Hsing (2)

(1) Purdue University, West Lafayette, IN, (2) University of Michigan, Ann Arbor, MI

Stilian Stoev  
University of Michigan

Tailen Hsing  
University of Michigan

Andrew Yarger  
Purdue University

Andrew Yarger  
N/A

The classical Matérn model has been a staple in spatial statistics. We offer a new perspective to extending the Matérn covariance model to the vector-valued setting. We adopt a spectral, stochastic integral approach, which allows us to address challenging issues on the validity of the covariance structure and at the same time to obtain new, flexible, and interpretable models. In particular, our multivariate extensions of the Matérn model allow for time-irreversible or, more generally, asymmetric covariance structures. Moreover, the spectral approach provides an essentially complete flexibility in modeling the local structure of the process. We establish closed-form representations of the cross-covariances when available, compare them with existing models, simulate Gaussian instances of these new processes, and demonstrate estimation of the model's parameters through maximum likelihood. An application of the new class of multivariate Matérn models to environmental data indicate their success in capturing inherent covariance-asymmetry phenomena.

Multivariate spatial statistics|cross-covariance functions|spectral analysis| | |

Section on Statistics and the Environment

Spatio-temporal statistics