adaptiveLassoEst() applied the adaptive LASSO to the
entries of the sample covariance matrix. The thresholding function is
inspired by the penalized regression introduced by
Zou (2006)
. The thresholding function assigns
a weight to each entry of the sample covariance matrix based on its
initial value. This weight then determines the relative size of the penalty
resulting in larger values being penalized less and reducing bias
(Rothman et al. 2009)
.
adaptiveLassoEst(dat, lambda, n)A numeric data.frame, matrix, or similar object.
A non-negative numeric defining the amount of
thresholding applied to each element of dat's sample covariance
matrix.
A non-negative numeric defining the exponent of the adaptive
weight applied to each element of dat's sample covariance matrix.
A matrix corresponding to the estimate of the covariance
matrix.
Rothman AJ, Levina E, Zhu J (2009).
“Generalized Thresholding of Large Covariance Matrices.”
Journal of the American Statistical Association, 104(485), 177-186.
doi: 10.1198/jasa.2009.0101
, https://doi.org/10.1198/jasa.2009.0101.
Zou H (2006).
“The Adaptive Lasso and Its Oracle Properties.”
Journal of the American Statistical Association, 101(476), 1418-1429.
doi: 10.1198/016214506000000735
, https://doi.org/10.1198/016214506000000735.
adaptiveLassoEst(dat = mtcars, lambda = 0.9, n = 0.9)
#> mpg cyl disp hp drat wt
#> mpg 36.291826 -9.0609940 -633.09474 -320.727511 1.791643 -4.9283324
#> cyl -9.060994 2.9013065 199.65332 101.918699 0.000000 0.7496917
#> disp -633.094743 199.6533192 15360.79969 6721.158375 -47.038454 107.6720667
#> hp -320.727511 101.9186995 6721.15838 4700.866530 -16.385270 44.1656064
#> drat 1.791643 0.0000000 -47.03845 -16.385270 0.000000 0.0000000
#> wt -4.928332 0.7496917 107.67207 44.165606 0.000000 0.1060738
#> qsec 4.298104 -1.4245844 -96.03823 -86.755340 0.000000 0.0000000
#> vs 1.581827 0.0000000 -44.35067 -24.942707 0.000000 0.0000000
#> am 1.322579 0.0000000 -36.53193 -8.198967 0.000000 0.0000000
#> gear 1.722184 0.0000000 -50.77876 -6.203983 0.000000 0.0000000
#> carb -5.182560 0.9586480 79.05272 83.020954 0.000000 0.0000000
#> qsec vs am gear carb
#> mpg 4.298104 1.581827 1.322579 1.722184 -5.182560
#> cyl -1.424584 0.000000 0.000000 0.000000 0.958648
#> disp -96.038229 -44.350668 -36.531926 -50.778756 79.052723
#> hp -86.755340 -24.942707 -8.198967 -6.203983 83.020954
#> drat 0.000000 0.000000 0.000000 0.000000 0.000000
#> wt 0.000000 0.000000 0.000000 0.000000 0.000000
#> qsec 2.905253 0.000000 0.000000 0.000000 -1.433437
#> vs 0.000000 0.000000 0.000000 0.000000 0.000000
#> am 0.000000 0.000000 0.000000 0.000000 0.000000
#> gear 0.000000 0.000000 0.000000 0.000000 0.000000
#> carb -1.433437 0.000000 0.000000 0.000000 2.263526