Nonstationary modeling for multivariate spatial processes

Nonstationary Multivariate Spatial Covariance Modeling

We derive a class of matrix valued covariance functions where the direct and crosscovariance functions are Matérn. The parameters of the Matérn class are allowed to vary with location, yielding local variances, local ranges, local geometric anisotropies and local smoothnesses. We discuss inclusion of a nonconstant cross-correlation coefficient and a valid approximation. Estimation utilizes kern...

A Generalized Convolution Model for Multivariate Nonstationary Spatial Processes

We propose a constructive method for specifying flexible classes of nonstationary stochastic models for multivariate spatial data. The method is based upon convolutions of spatially varying covariance functions and produces mathematically valid covariance structures. This method generalizes the convolution approach suggested by Majumdar and Gelfand (2007) to extend multivariate spatial covarian...

Modeling and Prediction of Nonstationary Spatial Processes

Spectral methods for nonstationary spatial processes

We propose a nonstationary periodogram and various parametric approaches for estimating the spectral density of a nonstationary spatial process. We also study the asymptotic properties of the proposed estimators via shrinking asymptotics, assuming the distance between neighbouring observations tends to zero as the size of the observation region grows without bound. With this type of asymptotic ...

Nonstationary cross-covariance models for multivariate processes on a globe

In geophysical and environmental problems, it is common to have multiple variables of interest measured at the same location and time. These multiple variables typically have dependence over space (and/or time). As a consequence, there is a growing interest in developing models for multivariate spatial processes, in particular, the cross-covariance models. On the other hand, many data sets thes...