Abstract
We introduce a regularization approach to 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 a computationally efficient method for solving the regularization problem and obtaining the optimal spatial predictions that require no high-dimensional matrix inversion. Some numerical examples are provided to demonstrate the effectiveness of the proposed method.