A restricted composite likelihood approach to modelling Gaussian geostatistical data

Composite likelihood methods have become popular in spatial statistics. This is mainly due to the fact that large matrices need to be inverted in full maximum likelihood and this becomes computationally expensive when you have a large number of regions under consideration. We introduce restricted pairwise composite likelihood (RECL) methods for estimation of mean and covariance parameters in a Gaussian random field, without resorting back to the full likelihood. A simulation study is carried out to investigate how this method works in settings of increasing domain as well as in-fill asymptotics, whilst varying the strength of correlation. Preliminary results showed that pairwise composite likelihoods tend to underestimate the variance parameters, especially when there is high correlation, while RECL corrects for the underestimation. Therefore, RECL is recommended if interest is in both the mean and the variance parameters.