A truncated pairwise likelihood approach for high-dimensional covariance estimation

Oregon Convention Center 

Pairwise likelihood allows inference for distributions with high-dimensional dependencies by combining marginal pairwise likelihood functions. In certain models, including the multivariate normal distribution, pairwise and full likelihoods are maximized by the same parameter values, thus retaining the same statistical efficiency when the number of variables is fixed. We propose to estimate sparse high-dimensional covariance matrices by maximizing a truncated pairwise likelihood function including only terms corresponding to nonzero covariance elements. Pairwise likelihood truncation is obtained by minimizing the distance between pairwise and full likelihood scores plus a L1-penalty discouraging the inclusion of relatively noisy terms. Differently from other regularization approaches, our penalty focuses on whole pairwise likelihood objects rather than on individual parameters, thus retaining unbiased estimating equations. Our asymptotic analysis shows that the resulting estimator has the same efficiency as the oracle maximum likelihood estimator based on the knowledge of the nonzero covariance entries. The properties of the new method are confirmed by numerical examples.

Composite likelihood

High-dimensional covariance

L1-penalty

Pairwise likelihood

Sparse covariance 

IMS