linearShrinkEst() computes the linear shrinkage estimate of the covariance matrix for a given value of alpha. The linear shrinkage estimator is defined as the convex combination of the sample covariance matrix and the identity matrix. The choice of alpha determines the bias-variance tradeoff of the estimators in this class: values near 1 are more likely to exhibit high variance but low bias, and values near 0 are more likely to be be very biased but have low variance.

linearShrinkEst(dat, alpha)

Arguments

dat

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

alpha

A numeric between 0 and 1 defining convex combinations of the sample covariance matrix and the identity. alpha = 1 produces the sample covariance matrix, and alpha = 0 returns the identity.

Value

A matrix corresponding to the estimate of the covariance matrix.

Examples

linearShrinkEst(dat = mtcars, alpha = 0.1)
#>              mpg         cyl        disp          hp         drat          wt
#> mpg    4.5324103 -0.91723790  -63.309721 -32.0732056  0.219506351 -0.51166847
#> cyl   -0.9172379  1.21895161   19.966028  10.1931452 -0.066836694  0.13673710
#> disp -63.3097208 19.96602823 1536.979983 672.1158669 -4.706401915 10.76842040
#> hp   -32.0732056 10.19314516  672.115867 470.9866935 -1.645110887  4.41926613
#> drat   0.2195064 -0.06683669   -4.706402  -1.6451109  0.928588135 -0.03727207
#> wt    -0.5116685  0.13673710   10.768420   4.4192661 -0.037272073  0.99573790
#> qsec   0.4509149 -0.18868548   -9.605168  -8.6770081  0.008714073 -0.03054816
#> vs     0.2017137 -0.07298387   -4.437762  -2.4987903  0.011864919 -0.02736613
#> am     0.1803931 -0.04657258   -3.656401  -0.8320565  0.019015121 -0.03381048
#> gear   0.2135685 -0.06491935   -5.080262  -0.6358871  0.027598790 -0.04210806
#> carb  -0.5363105  0.15201613    7.906875   8.3036290 -0.007840726  0.06757903
#>              qsec           vs           am        gear         carb
#> mpg   0.450914919  0.201713710  0.180393145  0.21356855 -0.536310484
#> cyl  -0.188685484 -0.072983871 -0.046572581 -0.06491935  0.152016129
#> disp -9.605168145 -4.437762097 -3.656401210 -5.08026210  7.906875000
#> hp   -8.677008065 -2.498790323 -0.832056452 -0.63588710  8.303629032
#> drat  0.008714073  0.011864919  0.019015121  0.02759879 -0.007840726
#> wt   -0.030548161 -0.027366129 -0.033810484 -0.04210806  0.067579032
#> qsec  1.219316613  0.067056452 -0.020495968 -0.02804032 -0.189411290
#> vs    0.067056452  0.925403226  0.004233871  0.00766129 -0.046370968
#> am   -0.020495968  0.004233871  0.924899194  0.02923387  0.004637097
#> gear -0.028040323  0.007661290  0.029233871  0.95443548  0.032661290
#> carb -0.189411290 -0.046370968  0.004637097  0.03266129  1.160887097