Sparse composite likelihood selection

Composite likelihood has shown promise in settings with large num- ber of parameters p due to its ability to break down complex models into simpler components, even when the full likelihood is intractable. However, there does not seem to exist agreement on how to construct composite functions that are computationally e cient and statistically sound when p is allowed to diverge. We present a exible method to select sparse composite likelihoods via a criterion representing the statistical e ciency of the implied estimator and an L1-penalty discouraging the inclusion of too many sub-likelihood terms. The theoretical properties of the proposed procedure are illustrated through simulation studies.