scadEst() applies the SCAD thresholding function of
Fan and Li (2001)
to each entry of the sample
covariance matrix. This penalized estimator constitutes a compromise
between hard and soft thresholding of the sample covariance matrix: it is
a linear interpolation between soft thresholding up to 2 * lambda
and hard thresholding after 3.7 * lambda
(Rothman et al. 2009)
.
scadEst(dat, lambda)A numeric data.frame, matrix, or similar object.
A non-negative numeric defining the degree of
thresholding applied to each element of dat's sample covariance
matrix.
A matrix corresponding to the estimate of the covariance
matrix.
Fan J, Li R (2001).
“Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties.”
Journal of the American Statistical Association, 96(456), 1348-1360.
doi: 10.1198/016214501753382273
, https://doi.org/10.1198/016214501753382273.
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.
scadEst(dat = mtcars, lambda = 0.2)
#> mpg cyl disp hp drat wt
#> mpg 36.324103 -9.1723790 -633.09721 -320.732056 2.19506351 -5.11668468
#> cyl -9.172379 3.1895161 199.66028 101.931452 -0.62622984 1.36737097
#> disp -633.097208 199.6602823 15360.79983 6721.158669 -47.06401915 107.68420403
#> hp -320.732056 101.9314516 6721.15867 4700.866935 -16.45110887 44.19266129
#> drat 2.195064 -0.6262298 -47.06402 -16.451109 0.08588135 -0.17272073
#> wt -5.116685 1.3673710 107.68420 44.192661 -0.17272073 0.95737897
#> qsec 4.509149 -1.8868548 -96.05168 -86.770081 0.00000000 -0.10548161
#> vs 2.017137 -0.7238615 -44.37762 -24.987903 0.00000000 -0.07366129
#> am 1.803931 -0.3043880 -36.56401 -8.320565 0.00000000 -0.13810484
#> gear 2.135685 -0.5957780 -50.80262 -6.358871 0.07598790 -0.23348102
#> carb -5.363105 1.5201613 79.06875 83.036290 0.00000000 0.63801992
#> qsec vs am gear carb
#> mpg 4.509149194 2.01713710 1.803931452 2.13568548 -5.3631048
#> cyl -1.886854839 -0.72386148 -0.304388046 -0.59577799 1.5201613
#> disp -96.051681452 -44.37762097 -36.564012097 -50.80262097 79.0687500
#> hp -86.770080645 -24.98790323 -8.320564516 -6.35887097 83.0362903
#> drat 0.000000000 0.00000000 0.000000000 0.07598790 0.0000000
#> wt -0.105481613 -0.07366129 -0.138104839 -0.23348102 0.6380199
#> qsec 3.193166129 0.62972011 -0.004959677 -0.08040323 -1.8941129
#> vs 0.629720114 0.05403226 0.000000000 0.00000000 -0.3011860
#> am -0.004959677 0.00000000 0.048991935 0.09233871 0.0000000
#> gear -0.080403226 0.00000000 0.092338710 0.42926945 0.1266129
#> carb -1.894112903 -0.30118596 0.000000000 0.12661290 2.6088710