Sparse composite likelihood selection

TL;DR

This paper proposes a method for selecting sparse composite likelihoods in high-dimensional settings by balancing statistical efficiency and model simplicity through an $L_1$-penalized criterion.

Contribution

It introduces a novel selection procedure for composite likelihood components that is computationally efficient and statistically consistent in diverging parameter scenarios.

Findings

The method effectively identifies relevant sub-likelihoods.

The procedure achieves consistent model selection under certain conditions.

Applications to real data demonstrate practical utility.

Abstract

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.