"Linear Ridge Estimator of High-Dimensional Precision Matrix Using Random Matrix Theory"

Ito, Tsubasa and Tatsuya Kubokawa

November 2015

In estimation of the large precision matrix, this paper suggests a new shrinkage estimator, called the linear ridge estimator. This estimator is motivated from a Bayesian aspect for a spike and slab prior distribution of the precision matrix, and has a form of convex combination of the ridge estimator and the identity matrix multiplied by scalar. The optimal parameters in the linear ridge estimator are derived in terms of minimizing a Frobenius loss function and estimated in closed forms based on the random matrix theory. Finally, the performance of the linear ridge estimator is numerically investigated and compared with some existing estimators.