InvCovShrinkBGP16: Linear shrinkage estimator of the inverse covariance matrix...

In HDShOP: High-Dimensional Shrinkage Optimal Portfolios

Linear shrinkage estimator of the inverse covariance matrix \insertCiteBGP2016HDShOP

Description

The optimal linear shrinkage estimator of the inverse covariance (precision) matrix that minimizes the Frobenius norm is given by:

\hat{Π}_{OLSE} = \hat{α} \hat{Π} + \hat{β} Π_0,

where \hat{α} and \hat{β} are optimal shrinkage intensities given in Eq. (4.4) and (4.5) of \insertCiteBGP2016HDShOP. \hat{Π} is the inverse of the sample covariance matrix (iSCM) and Π_0 is a positive definite symmetric matrix used as the target matrix (TM), for example, I.

Usage

InvCovShrinkBGP16(n, p, TM, iSCM)

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

Value

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

References

\insertAllCited

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]

HDShOP documentation built on Nov. 10, 2022, 5:12 p.m.