  We present a new method for estimating multivariate, second-order stationary
Gaussian Random Field (GRF) models based on the Sparse Precision matrix
Selection (SPS) algorithm, proposed by Davanloo et al. (2015) for estimating
scalar GRF models. Theoretical convergence rates for the estimated
between-response covariance matrix and for the estimated parameters of the
underlying spatial correlation function are established. Numerical tests using
simulated and real datasets validate our theoretical findings. Data
segmentation is used to handle large data sets.
