covShrink: Shrinkage Estimation of the Covariance Matrix

In abnormally-distributed/cvreg: Cross Validation and Robust Estimation Utilities

Description

This implements the covariance estimator of Schaefer & Strimmer (2005) which in turn builds upon Ledoit & Wolf's (2004) paper. Shrinkage targets A, B, and D of Schaefer & Strimmer's (2005) paper are offered here, details of which are given below:

Target A: Identity (diagonal, unit variance). Off-diagonal entries are shrunk towards zero, while diagonal entries are shrunk towards 1.

Target B: Pooled (diagonal, common-variance). Off diagonals are shrunk as in Target A, but diagonal entries are shrunk towards a common value. In this package, the geometric mean is utilized. Schaefer & Strimmer use the median, but the geometric mean is a good choice because it is preferable to the arithmetic mean when data are > 0 (which variances are) and is robust to outlying observations while still accounting for them in its estimate. This is the default shrinkage target.

Target D: Unequal (diagonal, empirical variances). This works just as Target B, but the mixing parameter for the diagonal is set to zero, such that the empirical variances are along the diagonal. If you have reason to believe the variances of your covariates should be more similar than different, this is a recommended choice.

Targets C, E, and F are not offered due to the fact that they do not guarantee a positive-definite covariance matrix.

Also available here is an adaptive non-linear shrinkage procedure. The estimator was adapted from the nlshrink package, but with a few minor adjustments to simplify the useage and speed up the estimation. Note that the penalization method for this is entirely different and based on a non-linear optimization problem. For details, see Ledoit & Wolf (2015).

Usage

covShrink(
  x,
  w = NULL,
  alpha = NULL,
  alpha.var = NULL,
  target = c("unequal", "identity", "pooled", "adaptive"),
  ...
)

Arguments

x	a data frame or matrix of numeric covariates
alpha	a custom value for the off-diagonal mixing parameter. if left as NULL the optimal value will automatically be selected.
alpha.var	a custom value for the diagonal mixing parameter. if left as NULL the optimal value will automatically be selected.
target	one of "unequal" (the default), "identity", "pooled", or "adaptive".
...	other arguments

Value

a covariance matrix

References

Schaefer, J. ; K. Strimmer (2005) A shrinkage approach to large-scale covariance estimation and implications for functional genomics. Statist. Appl. Genet. Mol. Biol. 4:32.

Ledoit, O. ; M. Wolf (2004). Honey, I shrunk the sample covariance matrix. J. Portfolio Management, 30(4), 110-119, doi: 10.3905/jpm.2004.110

Ledoit, O. ; Wolf, M. (2015). Spectrum estimation: a unified framework for covariance matrix estimation and PCA in large dimensions. Journal of Multivariate Analysis, 139(2)

abnormally-distributed/cvreg documentation built on May 3, 2020, 3:45 p.m.