A Note on Information Bias and Efficiency of Composite Likelihood

Abstract

The properties of inference based on composite likelihood (CL) are wellestablished, but can be surprising, and intuition based on likelihood inference can be misleading. In this note, we show by example that the variance of a maximum composite likelihood estimator (MCLE) can increase when nuisance parameters are known, rather than estimated; that estimators based on more independent component likelihoods can be less efficient than those based on fewer; and that incorporating higher-dimensional marginal densities can also lead to less efficient inference. The role of information bias is highlighted to understand the occurrence of these paradoxical phenomena.