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.
nlShrinkLWEst(dat)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. https://EconPapers.repec.org/RePEc:zur:econwp:264.
nlShrinkLWEst(dat = mtcars)
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 63.602387 -17.3756215 -1239.06580 -615.53668 4.0388075 -9.4366996
#> [2,] -17.375622 5.9552274 390.95557 195.09993 -1.2821077 2.7089340
#> [3,] -1239.065804 390.9555684 29716.52575 13567.68688 -89.7284694 207.4037721
#> [4,] -615.536679 195.0999307 13567.68688 8199.93035 -36.2488721 91.3619556
#> [5,] 4.038807 -1.2821077 -89.72847 -36.24887 0.4565959 -0.6705492
#> [6,] -9.436700 2.7089340 207.40377 91.36196 -0.6705492 1.7305492
#> [7,] 8.963471 -3.3492280 -200.17922 -142.37336 0.3596440 -0.9676052
#> [8,] 3.867541 -1.3369177 -87.64399 -46.36226 0.2480242 -0.5599951
#> [9,] 3.194599 -0.9148006 -68.28263 -22.42837 0.3001023 -0.5808273
#> [10,] 3.941742 -1.2753715 -93.19644 -24.47009 0.4401702 -0.7157005
#> [11,] -9.437382 2.7979487 168.54917 132.14305 -0.3221904 1.3398349
#> [,7] [,8] [,9] [,10] [,11]
#> [1,] 8.96347131 3.8675414 3.19459905 3.94174218 -9.4373816
#> [2,] -3.34922796 -1.3369177 -0.91480063 -1.27537154 2.7979487
#> [3,] -200.17921923 -87.6439882 -68.28262772 -93.19644414 168.5491733
#> [4,] -142.37336090 -46.3622632 -22.42836949 -24.47009443 132.1430534
#> [5,] 0.35964402 0.2480242 0.30010235 0.44017017 -0.3221904
#> [6,] -0.96760523 -0.5599951 -0.58082733 -0.71570051 1.3398349
#> [7,] 4.35735469 1.0392228 -0.04402801 -0.06795678 -2.7015133
#> [8,] 1.03922282 0.4412793 0.15738797 0.19755856 -0.7719914
#> [9,] -0.04402801 0.1573880 0.39265386 0.41375692 -0.1193703
#> [10,] -0.06795678 0.1975586 0.41375692 0.75705605 0.1533120
#> [11,] -2.70151325 -0.7719914 -0.11937035 0.15331198 3.5903329