Generalized Sparse Precision Matrix Selection for Fitting Multivariate Gaussian Random Fields to Large Data Sets
This work addresses the challenge of fitting multivariate spatial models to large datasets, which is incremental as it builds on an existing method for scalar models.
The authors tackled the problem of estimating multivariate Gaussian Random Field models for large datasets by extending the Sparse Precision matrix Selection algorithm, achieving theoretical convergence rates for covariance matrix and parameter estimates validated through numerical tests.
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.