sigma_estim_evc_mp: Eigenvalue Clipping Covariance Estimation (Marcenko-Pastur)

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

Description

Computes the eigenvalue clipping estimator of the covariance matrix with the Marcenko-Pastur edge.

Usage

sigma_estim_evc_mp(data)

Arguments

data	an nxp data matrix

Details

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

\hat{Σ}=Δ\hat{Λ}Δ',

where Δ is the matrix with the sample eigenvectors of the data matrix and \hat{Λ} 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

λ_{min, max}=(1\mp√{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 λ_{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(sp200)
sp_rets <- sp200[,-1]
sigma_evc_mp <- sigma_estim_evc_mp(sp_rets)[[1]]

antshi/CovEstim documentation built on Nov. 13, 2020, 2:25 p.m.