Multi-target Linear Shrinkage Estimation Of Large Precision Matrix

Precision matrix is very important in many disciplines such as financial engineering,biological genetics,and wireless communication.For example,if the precision matrix is known,we,can estimate different types of optimal portfolios very well.But in reality,the true precision matrix is unknown,so it needs to be estimated.When the dimension p of the covariance matrix is much smaller than the sample size n,many existing research results show that the inverse of the sample covariance matrix is the consistent estimator of the precision matrix.However,under normality assumption if p/n?c ?(0,1),then E(Sn-1)=n/n-p-2?n-1,so the inverse of the sample covariance matrix does not estimate the precision matrix well.In this case,many articles have tried to solve t.his problem.This problem can be considered by a single target linear shrinkage estimator.The single target linear shrinkage estimator can be regarded as a special Ridge type estimator,but its performance is affected by the selection of target matrix.If the selection of the target matrix is inappropriate,the performance of the single,target linear shrinkage estimator will be poor.In order to overcome this shortcoming and reduce estimation error caused by improper selection of target matrix,this paper considers a set of target matrices,and under the loss of Frobenius Norm,by shrinking Sn-1 directly,we obtain the multi-target linear shrinkage estimator of the precision matrix,which is convenient to calculate.It can be seen from the results of numerical simulation and empirical analysis that the performance of the multi-target linear shrinkage estimator is very good.