cov_estim_evc_mp: Eigenvalue Clipping Covariance Estimation (Marcenko-Pastur)

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

Eigenvalue Clipping Covariance Estimation (Marcenko-Pastur)

Description

Computes the Eigenvalue Clipping (EVC) estimator of the covariance matrix with the Marcenko-Pastur (MP) edge.

Usage

cov_estim_evc_mp(data)

Arguments

data	an nxp data matrix

Details

The eigenvalue clipping covariance matrix estimator is computed with the following formula:

\hat{\Sigma}=\Delta\hat{\Lambda}\Delta',

where \Delta is the matrix with the sample eigenvectors of the data matrix and \hat{\Lambda} is a diagonal matrix with the "clipped" sample eigenvalues. The clipping procedure follows \insertCitelaloux1999;textualcovestim. In particular, when assuming i.i.d returns, the eigenvalues of the sample correlation matrix are distributed according to a Marcenko-Pastur distribution \insertCitemarvcenko1967distributioncovestim with

\lambda_{min, max}=(1\mp\sqrt{p/n})^2

as the smallest and largest eigenvalues of a random correlation matrix. Therefore, only eigenvalues which lie outside this interval can bring useful information. In this eigenvalue clipping procedure the sample eigenvalues bigger that \lambda_{max} are kept and the rest are substituted with their average as in \insertCitebouchaudpotters2009;textualcovestim.

Value

a list with the following entries

• a pxp estimated covariance matrix.

• an estimation specific tuning parameter, here an NA.

References

\insertAllCited

Examples

data(rets_m)
sigma_evc_mp <- cov_estim_evc_mp(rets_m)[[1]]

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