Sparse composite likelihood selection
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Composite likelihood has shown promise in settings where the number of parameters p is large due to its ability to break down complex models into simpler components, thus enabling inference even when the full likelihood is not tractable. Although there are a number of ways to formulate a valid composite likelihood in the finite-p setting, there does not seem to exist agreement on how to construct composite likelihoods that are comp utationally efficient and statistically sound when p is allowed to diverge. This article introduces a method to select sparse composite likelihoods by minimizing a criterion representing the statistical efficiency of the implied estimator plus an L_1-penalty discouraging the inclusion of too many sub-likelihood terms. Conditions under which consistent model selection occurs are studied. Examples illustrating the procedure are analysed in detail and applied to real data.
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