Abstract: Maximum composite likelihood estimation is an attractive and commonly used alternative to standard maximum likelihood estimation that typically involves sacrificing statistical efficiency for computational efficiency. This statistical efficiency can be quantified by evaluating the sandwich information matrix of the maximum composite likelihood estimator, and then comparing it with the analogous Fisher information matrix for the maximum likelihood estimator. In this paper, we derive new closed-form expressions for the asymptotic relative efficiency of various maximum composite likelihood estimators for a one-dimensional exponential covariance Gaussian process. These expressions are based on a sampling scheme that allows for analyses under three common spatial asymptotic frameworks: expanding domain, infill, and hybrid. Our results demonstrate how the choice of composite likelihood affects the estimation efficiency and consistency, particularly for the infill and hybrid frameworks.

Key words and phrases: Block likelihood, expanding domain, full conditional likelihood, hybrid asymptotics, infill asymptotics, sandwich covariance matrix.