On approximating optimal weighted composite likelihood method for spatial models

Conventional likelihood-based model inference methods, such as maximum likelihood estimation and Bayesian inference, are computationally expensive for many spatial models with large data sets. As an alternative inference tool, composite likelihood (CL) methods have gained considerable attention in recent years because of their simplicity and sound asymptotic properties. However, CL estimators often result in substantial loss in statistical efficiency with respect to maximum likelihood estimation. In this paper, we propose a new weight function to construct CL for the inference of spatial Gaussian process models. This weight function approximates the optimal weight derived from the theory of estimating equations. It combines block-diagonal approximation and the tapering strategy to facilitate computations. Gains in statistical and computational efficiency over existing CL methods are illustrated through simulation studies. (c) 2018 John Wiley & Sons, Ltd.