denseLinearShrinkEst() computes the asymptotically
optimal convex combination of the sample covariance matrix and a dense
target matrix. This target matrix's diagonal elements are equal to the
average of the sample covariance matrix estimate's diagonal elements, and
its off-diagonal elements are equal to the average of the sample covariance
matrix estimate's off-diagonal elements. For information on this
estimator's derivation, see Ledoit and Wolf (2020)
and
Schäfer and Strimmer (2005)
.
denseLinearShrinkEst(dat)A numeric data.frame, matrix, or similar object.
A matrix corresponding to the estimate of the covariance
matrix.
Ledoit O, Wolf M (2020).
“The Power of (Non-)Linear Shrinking: A Review and Guide to Covariance Matrix Estimation.”
Journal of Financial Econometrics.
ISSN 1479-8409, doi: 10.1093/jjfinec/nbaa007
, nbaa007, https://academic.oup.com/jfec/advance-article-pdf/doi/10.1093/jjfinec/nbaa007/33416890/nbaa007.pdf.
Schäfer J, Strimmer K (2005).
“A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics.”
Statistical Applications in Genetics and Molecular Biology, 4(1).
doi: 10.2202/1544-6115.1175
, https://www.degruyter.com/view/journals/sagmb/4/1/article-sagmb.2005.4.1.1175.xml.xml.
denseLinearShrinkEst(dat = mtcars)
#> mpg cyl disp hp drat wt
#> mpg 168.3510501 -0.5187563 -578.47011 -289.1213709 10.011084 3.238097
#> cyl -0.5187563 137.6579629 192.92621 102.3984642 7.358643 9.244379
#> disp -578.4701084 192.9262124 14363.65321 6233.8924274 -35.618377 107.727329
#> hp -289.1213709 102.3984642 6233.89243 4489.1902174 -7.261158 48.914117
#> drat 10.0110840 7.3586434 -35.61838 -7.2611579 134.968280 7.632505
#> wt 3.2380970 9.2443794 107.72733 48.9141173 7.632505 135.590299
#> qsec 12.1546578 6.2299390 -80.99642 -72.3987241 8.058482 7.694790
#> vs 9.8462679 7.3017012 -33.12992 -15.1689244 8.087669 7.724265
#> am 9.6487722 7.5463531 -25.89206 0.2702928 8.153902 7.664570
#> gear 9.9560812 7.3764040 -39.08150 2.0874403 8.233414 7.587709
#> carb 3.0098341 9.3859115 81.22039 84.8955800 7.905132 8.603757
#> qsec vs am gear carb
#> mpg 12.154658 9.846268 9.6487722 9.956081 3.009834
#> cyl 6.229939 7.301701 7.5463531 7.376404 9.385911
#> disp -80.996416 -33.129924 -25.8920555 -39.081502 81.220385
#> hp -72.398724 -15.168924 0.2702928 2.087440 84.895580
#> drat 8.058482 8.087669 8.1539023 8.233414 7.905132
#> wt 7.694790 7.724265 7.6645704 7.587709 8.603757
#> qsec 137.661344 8.598917 7.7879048 7.718020 6.223216
#> vs 8.598917 134.938778 8.0169812 8.048730 7.548221
#> am 7.787905 8.016981 134.9341092 8.248560 8.020716
#> gear 7.718020 8.048730 8.2485601 135.207709 8.280309
#> carb 6.223216 7.548221 8.0207164 8.280309 137.120102