Relative Asymptotic Efficiency of the Maximum Pseudolikelihood Estimate for Gauss–Markov Random Fields

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A general version of the maximum pseudolikelihood estimate of parameters within the class of Gauss–Markov random fields is stated in a rigorous way. Its asymptotic properties, namely the consistency, the asymptotic normality, and the relative asymptotic efficiency are studied. Explicit formulas for the asymptotic covariance matrix are given, and a decrease of efficiency is proved. A numerical example is added to show that the efficiency can be improved by enlarging the range of the conditional distribution used in the estimator.

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