CovShrinkBGP14: Linear shrinkage estimator of the covariance matrix...

In HDShOP: High-Dimensional Shrinkage Optimal Portfolios

Linear shrinkage estimator of the covariance matrix \insertCiteBGP2014HDShOP

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 \insertCiteBGP2014;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)

Arguments

n	sample size.
TM	the target matrix for the shrinkage estimator.
SCM	sample covariance matrix.

Value

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

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/p
SCM <- Sigma_sample_estimator(X)
Sigma_shr <- CovShrinkBGP14(n=n, TM=TM, SCM=SCM)
Sigma_shr$S[1:6, 1:6]

HDShOP documentation built on May 29, 2024, 2:20 a.m.