Sequential marginal likelihood selection for the estimation of sparse correlation matrices

Estimation of high-dimensional sparse correlation matrices is performed by selecting relevant marginal likelihoods from a large set of candidates. Selection occurs by minimizing the distance between maximum likelihood and marginal composite likelihood score, plus a weighted L1-penalty which discourages the inclusion of noisy marginal likelihoods. The resulting parameter estimator involves a sequential thresholding mechanism, whereby the marginal estimates are set to zero based on the absolute value of their adjusted z-score. Inferential properties of the proposed procedure are illustrated via simulation experiments and the analysis of cell signaling data.