nlShrinkLWEst {cvCovEst}R Documentation

Analytical Non-Linear Shrinkage Estimator


nlShrinkLWEst() invokes the analytical estimator presented by Ledoit and Wolf (2018) for applying a nonlinear shrinkage function to the sample eigenvalues of the covariance matrix. The shrinkage function relies on an application of the Hilbert Transform to an estimate of the sample eigenvalues' limiting spectral density. This estimated density is computed with the Epanechnikov kernel using a global bandwidth parameter of n^(-1/3). The resulting shrinkage function pulls eigenvalues towards the nearest mode of their empirical distribution, thus creating a localized shrinkage effect rather than a global one.

We do not recommend that this estimator be employed when the estimand is the correlation matrix. The diagonal entries of the resulting estimate are not guaranteed to be equal to one.





A numeric data.frame, matrix, or similar object.


A matrix corresponding to the estimate of the covariance matrix.


Ledoit O, Wolf M (2018). “Analytical nonlinear shrinkage of large-dimensional covariance matrices.” Technical Report 264, Department of Economics - University of Zurich.


nlShrinkLWEst(dat = mtcars)

[Package cvCovEst version 0.3.5 Index]