HDShOP (version 0.1.5)

CovShrinkBGP14: Linear shrinkage estimator of the covariance matrix BGP2014HDShOP

Description

The optimal linear shrinkage estimator of the covariance matrix that minimizes the Frobenius norm: $$\hat{\Sigma}_{OLSE} = \hat{\alpha} S + \hat{\beta} \Sigma_0,$$ where \(\hat{\alpha}\) and \(\hat{\beta}\) are optimal shrinkage intensities given in Eq. (4.3) and (4.4) of BGP2014;textualHDShOP. \(S\) is the sample covariance matrix (SCM, see Sigma_sample_estimator) and \(\Sigma_0\) is a positive definite symmetric matrix used as the target matrix (TM), for example, \(\frac{1}{p} I\).

Usage

CovShrinkBGP14(n, TM, SCM)

Value

a list containing an object of class matrix (S) and the estimated shrinkage intensities \(\hat{\alpha}\) and \(\hat{\beta}\).

Arguments

n

sample size.

TM

the target matrix for the shrinkage estimator.

SCM

sample covariance matrix.

References

Examples

# Parameter setting
n<-3e2
c<-0.7
p<-c*n
mu <- rep(0, p)
Sigma <- RandCovMtrx(p=p)

# Generating observations
X <- t(MASS::mvrnorm(n=n, mu=mu, Sigma=Sigma))

# Estimation
TM <- matrix(0, nrow=p, ncol=p)
diag(TM) <- 1/p
SCM <- Sigma_sample_estimator(X)
Sigma_shr <- CovShrinkBGP14(n=n, TM=TM, SCM=SCM)
Sigma_shr$S[1:6, 1:6]