mean_bop19: BOP shrinkage estimator

In HDShOP: High-Dimensional Shrinkage Optimal Portfolios

BOP shrinkage estimator

Description

Shrinkage estimator of the high-dimensional mean vector as suggested in \insertCiteBOP2019;textualHDShOP. It uses the formula

\hat μ_{BOP} = \hat α \bar x + \hat β μ_0 \quad ,

where \hat α and \hat β are shrinkage coefficients given by Eq.(6) and Eg.(7) of \insertCiteBOP2019;textualHDShOP that minimize weighted quadratic loss for a given target vector μ_0 (shrinkage target). \bar x stands for the sample mean vector.

Usage

mean_bop19(x, mu_0 = rep(1, p))

Arguments

x	a p by n matrix or a data frame of asset returns. Rows represent different assets, columns – observations.
mu_0	a numeric vector. The target vector used in the construction of the shrinkage estimator.

Value

a numeric vector containing the 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_bop19(x=x)

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