Asymptotics of Maximum Composite Likelihood Estimation for Geostatistical Data

Abstract

Parameter estimation and inference in a geostatistical model is often made challenging due to the strong dependence between nearby observations. For large sample sizes, maximum likelihood estimation quickly becomes computationally expensive to perform, so other estimation approaches such as maximum composite likelihood estimation have been proposed as alternatives. In this thesis, we investigate the statistical and computational performance of maximum composite likelihood estimation relative to maximum likelihood estimation for the Gaussian exponential covariance model. As the main contribution of this work, we derive and analyse the exact closed-form expressions for the sandwich covariance matrix of various composite likelihoods in one-dimensional space. These new results are found under a hybrid asymptotic framework, which unifies the traditional expanding domain and infill frameworks seen in the geostatistical literature. We then demonstrate the practical implementation of maximum composite likelihood approaches for estimation and inference, as well as perform a data-motivated simulation study of their statistical performance in a two-dimensional setting with irregularly-spaced observations.