cov_estim_lwone: Ledoit-Wolf Covariance Estimation (Linear Shrinkage) II

In antshi/CovEstim: (High-dimensional) Covariance Estimation

Ledoit-Wolf Covariance Estimation (Linear Shrinkage) II

Description

Computes the Ledoit-Wolf linear shrinkage estimator of the covariance matrix towards the one-parameter matrix.

Usage

cov_estim_lwone(data, shrink_int = NULL, zeromean_log = FALSE)

Arguments

data	an nxp data matrix.
shrink_int	a double, indicating the shrinkage intensity. Default is the optimal shrinkage intensity as in \insertCiteledoit2004oneparam;textualcovestim.
zeromean_log	a logical, indicating whether the data matrix has zero means (TRUE) or not (FALSE). Default value is FALSE.

Details

The Ledoit-Wolf linear shrinkage estimator of the covariance matrix towards the diagonal matrix of equal variances is calculated with the following formula:

\hat{\Sigma}= s\Sigma_{T} + (1-s)\Sigma,

where \Sigma is the sample covariance matrix, s is the user-supplied or optimal shrinkage intensity and \Sigma_{T} is a diagonal matrix with the average sample variance \bar{\sigma}^2 on the diagonal. This covariance estimator assumes a zero correlation and equal variances as the underlying covariance structure of the data. A corresponding MATLAB code for the estimator can be accessed under https://www.econ.uzh.ch/en/people/faculty/wolf/publications.html.

Value

a list with the following entries

• a pxp estimated covariance matrix.

• an estimation specific tuning parameter, here the shrinkage intensity.

References

\insertAllCited

Examples

data(rets_m)
sigma_lwone <- cov_estim_lwone(rets_m)[[1]]

antshi/CovEstim documentation built on June 10, 2025, 3:11 a.m.