ShrnkSigE: Shrunken Covariance Estimate.

Description

Builds a well-conditioned shrunken estimate of a covariance matrix based on Fisher and Sun's (2011) estimates and generalizations of Ledoit and Wolf's (2004) optimal optimal shrunken covariance matrices.

Usage

ShrnkSigE(df, p , SigmaRank, Sigma=NULL, SigmaSr=NULL, check=TRUE, Trgt,
minp=20, numtol=sqrt(.Machine$double.eps), ...)

Arguments

Degrees of freedom of the original (unshrunken) covariance estimate.

Dimension of the covariance matrix.

SigmaRank

Rank of the original (unshrunken) covariance estimate.

Sigma

Original (unshrunken) covariance estimate.

SigmaSr

Matrix square-root of the original (unshrunken) covariance estimate, i.e. a matrix, SigmaSr, such that SigmaSr^T SigmaSr = Sigma, where Sigma is the original unshrunken covariance estimate.

Trgt

A string code with the target type used by the shrunken estimator. The alternatives are CnstDiag for a Ledoit-Wolf constant diagonal target, Idntty for a p-dimensional identity, and VarDiag for a diagonal

check

Boolean flag indicating if the symmetry and the sign of the Sigma eigenvalues should be check upfront.

minp

Minimum number of variables required for the estimation of the target intensity to be considered reliable. If the dimension of Sigma is below pmin, no shrunken estimate is computed and the original sample covariance is returned.

numtol

Numerical tolerance. All computed eigenvalues below numtol are considered equal to zero, and the rank of original shrunken estimate is adjusted acordingly.

...

Further arguments passed to or from other methods.

Value

An object of class ShrnkMat with a compact representation of the shrunken covariance estimator.

Details

ShrnkSigE can take as input an original unshrunken estimate of the covariance matrix or, in alternative, one matrix square-root, SigmaSr (e.g. the original, centered and scaled, data matrix), such that $SigmaSr^T SigmaSr = Sigma$. In problems with more variables than observations it is preferable to use a matrix square-root for reasons of memory and computational efficiency.

References

Ledoit, O. and Wolf, M. (2004) A well-conditioned estimator for large-dimensional covariance matrices., Journal of Multivariate Analysis, 88 (2), 365-411.