linshrink: Linear-shrinkage estimator of population eigenvalues.

Description Usage Arguments Value References Examples

Description

linshrink estimates the population eigenvalues from the sample eigenvalues by shrinking each sample eigenvalue towards the global mean based on a shrinkage factor. Details in referenced publications.

Usage

1
linshrink(X, k = 0)

Arguments

X

A data matrix.

k

(Optional) Non-negative integer less than ncol(X). If k == 0 (default), X is assumed to contain 1 class, which will be centered. If k >= 1, X is assumed to contain k classes, each of which has already been centered.

Value

A numeric vector of length ncol(X), containing the population eigenvalue estimates sorted in ascending order.

References

  • Ledoit, O. and Wolf, M. (2004). A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis, 88(2)

  • Ledoit, O. and Wolf, M. (2016). Numerical Implementation of the QuEST function. arXiv:1601.05870 [stat.CO]

Examples

1
2
linshrink(X = matrix(rnorm(1e4, mean = 5), nrow = 100, ncol = 100)) # 1 class; will be centered
linshrink(X = matrix(rnorm(1e4), nrow = 100, ncol = 100), k = 1) # 1 class; no centering


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