| mean_bop19 {HDShOP} | R Documentation |
BOP shrinkage estimator
Description
Shrinkage estimator of the high-dimensional mean vector as suggested in Bodnar et al. (2019). It uses the formula
\hat \mu_{BOP} = \hat \alpha \bar x + \hat \beta \mu_0,
where
\hat \alpha and \hat \beta are shrinkage coefficients given by
Eq.(6) and Eg.(7) of Bodnar et al. (2019) that minimize
weighted quadratic loss for a given target vector \mu_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
Bodnar T, Okhrin O, Parolya N (2019). “Optimal shrinkage estimator for high-dimensional mean vector.” Journal of Multivariate Analysis, 170, 63–79.
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, mu_0=rep(1,p))