On the frequency domain composite likelihood methods for estimating space-time covariance functions for large datasets

Abstract

Covariance function plays very important roles in modeling and in prediction of spatial data. For instance, many statistical inferences such as maximum likelihood estimation and best linear unbiased prediction involve covariance matrices which must be inverted and this evaluation is slow when the number of observations is large, and the complexity increases even further in a space-time context. In this paper, we propose approximation methods based on three types of frequency domain composite likelihoods for the estimation of spatial-temporal covariance functions: paired, differenced, and conditional composite likelihoods to overcome this problem. The proposed likelihoods involve computationally efficient and matrix-free Gaussian likelihood approximations that have been successful in fitting parametric space-time covariance functions for massive datasets. We conduct a simulation study to evaluate the performance of the proposed estimation methods from statistical and computational viewpoints. The frequency domain spectral composite likelihood estimates demonstrate better performance compared to the observation domain composite likelihoods. Furthermore, our numerical examples show that paired and conditional frequency domain composite likelihoods work better than differenced frequency domain composite likelihood from statistical point of view.