R/estimators.R
spikedSteinShrinkEst.RdspikedSteinShrinkEst() implements the asymptotically
optimal shrinkage estimator with respect to the Stein loss in a spiked
covariance matrix model. Informally, this model admits Gaussian
data-generating processes whose covariance matrix is a scalar multiple of
the identity, save for a few number of large "spikes". A thorough review of
this estimator, or more generally spiked covariance matrix estimation, is
provided in Donoho et al. (2018)
.
spikedSteinShrinkEst(dat, p_n_ratio, num_spikes = NULL, noise = NULL)A numeric data.frame, matrix, or similar object.
A numeric between 0 and 1 representing the asymptotic
ratio of the number of features, p, and the number of observations, n.
A numeric integer equal to or larger than one which
providing the known number of spikes in the population covariance matrix.
Defaults to NULL, indicating that this value is not known and must
be estimated.
A numeric representing the known scalar multiple of the
identity matrix giving the approximate population covariance matrix.
Defaults to NULL, indicating that this values is not known and must
be estimated.
A matrix corresponding to the covariance matrix estimate.
Donoho D, Gavish M, Johnstone I (2018). “Optimal shrinkage of eigenvalues in the spiked covariance model.” The Annals of Statistics, 46(4), 1742 -- 1778.
spikedFrobeniusShrinkEst(dat = mtcars, p_n_ratio = 0.1, num_spikes = 2L)
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 27.663147 -8.5966480 -633.37176 -320.952507 1.8380080 -4.3684649
#> [2,] -8.596648 3.1720621 199.67670 101.953292 -0.5776376 1.3759243
#> [3,] -633.371758 199.6766974 15360.69990 6721.151917 -47.0759740 107.7048410
#> [4,] -320.952507 101.9532921 6721.15192 4700.768676 -16.4566826 44.2090633
#> [5,] 1.838008 -0.5776376 -47.07597 -16.456683 0.6095344 -0.3369659
#> [6,] -4.368465 1.3759243 107.70484 44.209063 -0.3369659 1.2155651
#> [7,] 5.074470 -1.6193679 -96.02672 -86.790194 0.1888899 -0.5990458
#> [8,] 1.968804 -0.6231265 -44.37709 -24.997643 0.1228698 -0.3019109
#> [9,] 1.317145 -0.4118828 -36.58027 -8.326957 0.1301915 -0.2692398
#> [10,] 1.700204 -0.5290605 -50.81772 -6.363670 0.1931165 -0.3826658
#> [11,] -4.468215 1.4298557 79.09401 83.073872 -0.1283000 0.4741877
#> [,7] [,8] [,9] [,10] [,11]
#> [1,] 5.07447019 1.96880419 1.31714549 1.70020351 -4.46821455
#> [2,] -1.61936786 -0.62312646 -0.41188281 -0.52906052 1.42985570
#> [3,] -96.02671828 -44.37709273 -36.58027398 -50.81771930 79.09400796
#> [4,] -86.79019439 -24.99764286 -8.32695723 -6.36367032 83.07387231
#> [5,] 0.18888988 0.12286977 0.13019154 0.19311648 -0.12830000
#> [6,] -0.59904585 -0.30191093 -0.26923977 -0.38266576 0.47418772
#> [7,] 2.19518483 0.41942038 0.03326137 -0.08623014 -1.72780065
#> [8,] 0.41942038 0.60140834 0.08132900 0.09647834 -0.38221201
#> [9,] 0.03326137 0.08132900 0.57613904 0.19030401 0.02318283
#> [10,] -0.08623014 0.09647834 0.19030401 0.76682762 0.17556675
#> [11,] -1.72780065 -0.38221201 0.02318283 0.17556675 2.19784126