jaws.cov: The Jackstraw Weighted Shrinkage Estimation Method for...
In ncchung/jaws: Jackstraw Weighted Shrinkage Methods

Description Usage Arguments Details Value Author(s) References See Also Examples

Estimates a covariance matrix of m variables (rows) from n samples (columns), when m > n. Shrinkage estimators of principal component loadings are used to construct a high-dimensional covariance matrix. Although several options are available to control characteristics of jackstraw weighted shrinkage (see jaws.pca), the required inputs are the data matrix dat and the number of principal components r to be used.

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jaws.cov(dat, r = NULL, jaws.pca.obj = NULL,
  stat.shrinkage = "F-statistics", extra.shrinkage = NULL, verbose = TRUE,
  seed = NULL)

`dat`	a data matrix with `m` rows as variables and `n` columns as observations.
`r`	a number of significance principal components (`r < n`).
`jaws.pca.obj`	a jaws.pca output (optional).
`stat.shrinkage`	PNV shrinkage may be applied to "F-statistics" or "loadings" (default: F-statistics).
`extra.shrinkage`	extra shrinkage methods may be used; see details below (optional).
`verbose`	a logical specifying to print the progress (default: TRUE).
`seed`	a seed for the random number generator (optional).

By default, jaws.cov computes two canonical jackstraw weighted shrinkage estimators, namely PIP and PNV. Additionally, extra shrinkage techniques may apply, such as soft- or hard-thresholding posterior inclusion probabilities extra.shrinkage=c("PIPsoft","PIPhard"). Please provide r numerical threshold values to be applied to r principal components.

This algorithm applies shrinkage to the signal component of the covariance matrix, and assumes the independently distributed noise. Since this function relies on shrunken loadings of PCs, you may first run jaws.pca on dat with a greater control over optional arguments and supply its output jaws.pca.obj to this function.

jaws.cov returns a list consisting of

`PIP`	estimated covariance matrix based on posterior inclusion probabilities
`PNV`	estimated covariance matrix based on proportion of null variables

With appropriate extra.shrinkage options (for details, see the Supplementary Information of Chung and Storey (2013), the output may also include

`PIPhard`	estimated covariance matrix based on hard-thresholding the `PIP` loadings
`PIPsoft`	estimated covariance matrix based on soft-thresholding the `PIP` loadings

Neo Chung nchchung@gmail.com

Chung and Storey (2015) Forthcoming

jaws.pca jackstraw.PCA

set.seed(1234)
## simulate data from a latent variable model: Y = BX + E
B = c(rep(1,50),rep(-1,50), rep(0,900))
X = rnorm(20)
E = matrix(rnorm(1000*20), nrow=1000)
dat = B %*% t(X) + E
dat = t(scale(t(dat), center=TRUE, scale=FALSE))

## estimate large-scale covariance matrix
jaws.cov.out = jaws.cov(dat, r=1)