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Statistica Sinica 25 (2015), 151-171

NON-STATIONARY MULTIVARIATE SPATIAL COVARIANCE
ESTIMATION VIA LOW-RANK REGULARIZATION
ShengLi Tzeng and Hsin-Cheng Huang
China Medical University and Academia Sinica

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.

Key words and phrases: Fixed rank kriging, large data, spatial prediction.

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