poetEst() implements the Principal Orthogonal complEment
Thresholding (POET) estimator, a nonparametric, unobserved-factor-based
estimator of the covariance matrix (Fan et al. 2013)
. The
estimator is defined as the sum of the sample covariance matrix'
rank-k approximation and its post-thresholding principal orthogonal
complement. The hard thresholding function is used here, though others
could be used instead.
poetEst(dat, k, lambda)A numeric data.frame, matrix, or similar object.
An integer indicating the number of unobserved latent
factors. Empirical evidence suggests that the POET estimator is robust to
overestimation of this hyperparameter (Fan et al. 2013)
. In
practice, it is therefore preferable to use larger values.
A non-negative numeric defining the amount of
thresholding applied to each element of sample covariance matrix's
orthogonal complement.
A matrix corresponding to the estimate of the covariance
matrix.
Fan J, Liao Y, Mincheva M (2013). “Large covariance estimation by thresholding principal orthogonal complements.” Journal of the Royal Statistical Society. Series B (Statistical Methodology), 75(4), 603--680. ISSN 13697412, 14679868, https://www.jstor.org/stable/24772450.
poetEst(dat = mtcars, k = 2L, lambda = 0.1)
#> mpg cyl disp hp drat wt
#> mpg 36.324103 -9.1723790 -633.09721 -320.732056 2.19506351 -5.1166847
#> cyl -9.172379 3.1895161 199.68181 101.957810 -0.57764791 1.3759564
#> disp -633.097208 199.6818126 15360.79983 6721.151681 -47.07821023 107.7090659
#> hp -320.732056 101.9578102 6721.15168 4700.866935 -16.45539748 44.2081565
#> drat 2.195064 -0.5776479 -47.07821 -16.455397 0.28588135 -0.3369854
#> wt -5.116685 1.3759564 107.70907 44.208157 -0.33698538 0.9573790
#> qsec 4.509149 -1.8868548 -96.02405 -86.804075 0.08714073 -0.3054816
#> vs 1.968872 -0.7298387 -44.37791 -24.999372 0.12286905 -0.3019144
#> am 1.803931 -0.4118850 -36.58262 -8.324576 0.13020674 -0.2692619
#> gear 2.135685 -0.6491935 -50.82168 -6.358748 0.19314430 -0.3827046
#> carb -5.363105 1.4299448 79.09023 83.088899 -0.12824916 0.6757903
#> qsec vs am gear carb
#> mpg 4.50914919 1.96887209 1.80393145 2.13568548 -5.36310484
#> cyl -1.88685484 -0.72983871 -0.41188504 -0.64919355 1.42994485
#> disp -96.02404610 -44.37791164 -36.58261788 -50.82168281 79.09023204
#> hp -86.80407537 -24.99937226 -8.32457551 -6.35874793 83.08889861
#> drat 0.08714073 0.12286905 0.13020674 0.19314430 -0.12824916
#> wt -0.30548161 -0.30191440 -0.26926186 -0.38270459 0.67579032
#> qsec 3.19316613 0.67056452 -0.20495968 -0.28040323 -1.89411290
#> vs 0.67056452 0.25403226 0.08132497 0.09646868 -0.38225399
#> am -0.20495968 0.08132497 0.24899194 0.29233871 0.02326462
#> gear -0.28040323 0.09646868 0.29233871 0.54435484 0.32661290
#> carb -1.89411290 -0.38225399 0.02326462 0.32661290 2.60887097