基于Lasso惩罚的迹差损失方法高维协变量调整的稀疏精度矩阵估计（英文）

Adjusting for High-Dimensional Covariates in Sparse Precision Matrix Estimation by Lasso Penalized D-Trace Loss

本文运用两阶段估计程序给出了协变量调整的精度矩阵估计.首先,运用联合l1惩罚方法确定影响均值的相关协变量.然后,将估计出的回归系数用于估计多元次高斯模型的均值,并通过Lasso惩罚的迹差损失方法对稀疏精度矩阵进行估计.在一些假设条件下,建立了精度矩阵估计的不同范数的收敛速率,并证明了依概率1收敛的稀疏恢复性质.数值结果表明,在有限样本情况下,同其他方法相比,我们的方法具有一定的优越性.

This paper develops a covariate-adjusted precision matrix estimation using a two-stage estimation procedure.Firstly,we identify the relevant covariates that a ect the means by a joint`1 penalization.Then,the estimated regression coe cients are used to estimate the mean values in a multivariate sub-Gaussian model in order to estimate the sparse precision matrix through a Lasso penalized D-trace loss.Under some assumptions,we establish the convergence rate of the precision matrix estimation under di erent norms and demonstrate the sparse recovery property with probability converging to one.Simulation shows that our methods have the nite-sample performance compared with other methods.