Precision Matrix Estimation With ROPE
提出一种岭型算子ROPE，通过惩罚似然函数（以Frobenius范数为惩罚项）来估计精度矩阵，并给出显式闭式解，类似回归中的岭回归。模拟和实际数据验证了其性能。
It is known that the accuracy of the maximum likelihood-based covariance and precision matrix estimates can be improved by penalized log-likelihood estimation. In this article, we propose a ridge-type operator for the precision matrix estimation, ROPE for short, to maximize a penalized likelihood function where the Frobenius norm is used as the penalty function. We show that there is an explicit closed form representation of a shrinkage estimator for the precision matrix when using a penalized log-likelihood, which is analogous to ridge regression in a regression context. The performance of the proposed method is illustrated by a simulation study and real data applications. Computer code used in the example analyses as well as other supplementary materials for this article are available online.