Joint Modeling for Mean Vector and Covariance Estimation with l1-Penalty

Abstract

In this study, we develop a novel updating-based method for penalized estimators for the mean vector and the covariance matrix. With a linear combination of predictors, the coefficients can be estimated by maximizing a penalized log likelihood function, and using coordinate descent algorithm is used to handle the l1-penalized function. In order to estimate the inverse covariance matrix estimation, we adopt a modified Cholesky decomposition so that to guarantee the positive definiteness of the estimators. In the genomic data analysis setting, we show that the proposed method can be efficiently used to detect the conditional independence among a group of genes, while adjusting for shared genetic effects. Simulation experiments benchmark the performance of the proposed method against another existing method.