mean_js {HDShOP}

James-Stein shrinkage estimator of the mean vector

Description

James-Stein shrinkage estimator of the mean vector as suggested in Jorion (1986). The estimator is given by

\hat \mu_{JS} = (1-\beta) \bar x + \beta Y_0 1,

where \bar x is the sample mean vector, \beta is the shrinkage coefficient which minimizes a quadratic loss given by Eq.(11) in Jorion (1986). Y_0 is a prespecified value.

Usage

mean_js(x, Y_0 = 1)

Arguments

x

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

Y_0

a numeric variable. Shrinkage target coefficient.

Value

a numeric vector containing the James-Stein shrinkage estimator of the mean vector.

References

Jorion P (1986). “Bayes-Stein estimation for portfolio analysis.” Journal of Financial and Quantitative Analysis, 279–292.

Examples

n<-7e2 # number of realizations
p<-.5*n # number of assets
x <- matrix(data = rnorm(n*p), nrow = p, ncol = n)
mm <- mean_js(x=x, Y_0 = 1)