Non-stationary Multivariate Spatial Covariance Estimation via Low-Rank Regularization

Abstract

We introduce a regularization approach for multivariate spatial covariance estimation based on a spatial random effect model. The proposed method is flexible to incorporate not only spatial non-stationarity but also asymmetry in spatial cross-covariances. By introducing a regularization term in the objective function, our method automatically produces a low-rank covariance estimate that effectively controls estimation variability even when the number of parameters is large. In addition, we offer computationally efficient methods for solving the regularization problem and obtaining the optimal spatial predictions, which require no high-dimensional matrix inversion. Some numerical examples are provided to demonstrate the effectiveness of the proposed method. 1 Statistica Sinica: Preprint doi:10.5705/ss.2013.211w