HDShOP (version 0.1.5)

InvCovShrinkBGP16: Linear shrinkage estimator of the inverse covariance matrix BGP2016HDShOP

Description

The optimal linear shrinkage estimator of the inverse covariance (precision) matrix that minimizes the Frobenius norm is given by: $$\hat{\Pi}_{OLSE} = \hat{\alpha} \hat{\Pi} + \hat{\beta} \Pi_0,$$ where \(\hat{\alpha}\) and \(\hat{\beta}\) are optimal shrinkage intensities given in Eq. (4.4) and (4.5) of BGP2016;textualHDShOP. \(\hat{\Pi}\) is the inverse of the sample covariance matrix (iSCM) and \(\Pi_0\) is a positive definite symmetric matrix used as the target matrix (TM), for example, I.

Usage

InvCovShrinkBGP16(n, p, TM, iSCM)

Value

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

Arguments

n

the number of observations

p

the number of variables (rows of the covariance matrix)

TM

the target matrix for the shrinkage estimator

iSCM

the inverse of the 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
iSCM <- solve(Sigma_sample_estimator(X))
Sigma_shr <- InvCovShrinkBGP16(n=n, p=p, TM=TM, iSCM=iSCM)
Sigma_shr$S[1:6, 1:6]