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 to 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 analysis under three commonly considered spatial asymptotic frameworks: expanding domain, infill and hybrid. Our results demonstrate how the choice of composite likelihood affects estimation efficiency and consistency, particularly with respect to the infill and hybrid frameworks.

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