mean_bs: Bayes-Stein shrinkage estimator of the mean vector

In HDShOP: High-Dimensional Shrinkage Optimal Portfolios

Bayes-Stein shrinkage estimator of the mean vector

Description

Bayes-Stein shrinkage estimator of the mean vector as suggested in \insertCiteJorion1986;textualHDShOP. The estimator is given by

\hat μ_{BS} = (1-β) \bar x + β Y_0 1 \quad ,

where \bar x is the sample mean vector, β and Y_0 are derived using Bayesian approach (see Eq.(14) and Eq.(17) in \insertCiteJorion1986;textualHDShOP).

Usage

mean_bs(x)

Arguments

x	a p by n matrix or a data frame of asset returns. Rows represent different assets, columns – observations.

Value

a numeric vector containing the Bayes-Stein shrinkage estimator of the mean vector

References

\insertAllCited

Examples

n <- 7e2 # number of realizations
p <- .5*n # number of assets
x <- matrix(data = rnorm(n*p), nrow = p, ncol = n)
mm <- mean_bs(x=x)

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