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)

Arguments

dat

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

k

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.

lambda

A non-negative numeric defining the amount of thresholding applied to each element of sample covariance matrix's orthogonal complement.

Value

A matrix corresponding to the estimate of the covariance matrix.

References

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.

Examples

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