On the robustness of maximum composite likelihood estimate

Composite likelihood methods have been receiving growing interest in a number of different application areas, where the likelihood function is too cumbersome to be evaluated. In the present paper, some theoretical properties of the maximum composite likelihood estimate (MCLE) are investigated in more detail. Robustness of consistency of the MCLE is studied in a general setting, and clarified and illustrated through some simple examples. We also carry out a simulation study of the performance of the MCLE in a constructed model suggested by Arnold (2010) that is not multivariate normal, but has multivariate normal marginal distributions.