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.

翻译：在参数数大的情况下,由于能够将复杂模型分为更简单的部分,因此有可能作出推断,即使不可能完全推理出这种可能性。虽然在限定-p美元的情况下有一些方法可以制定有效的复合可能性,但在允许美元差异时,对于如何构建计算使用效率高和统计性健全的复合可能性,似乎没有一致意见。本条款引入了一种选择稀薄复合可能性的方法,即尽可能减少隐含估计值的统计效率标准,加上1美元的罚款,以阻止列入过多的次级类似条件。研究的是一致选择模式所依据的条件,详细分析并应用于真实数据。