Covariate-adjusted precision matrix estimation with an application in genetical genomics

minimization, which can be easily implemented by linear programming. Asymptotic convergence rates in various matrix norms and sign consistency are established for the estimators of the regression coefficients and the precision matrix, allowing both the number of genes and the number of the genetic variants to diverge. Simulation shows that the proposed method results in significant improvements in both precision matrix estimation and graphical structure selection when compared to the standard Gaussian graphical model assuming constant means. The proposed method is also applied to analyze a yeast genetical genomics data for the identification of the gene network among a set of genes in the mitogen-activated protein kinase pathway.