eigen.est: Estimation of the leading eigenvalues of \mathbf{Sigma} under...

In trambakbanerjee/casp: Coordinate-wise Adaptive Shrinkage Prediction

Estimation of the leading eigenvalues of \mathbf{Σ} under a spiked covariance model

Description

Provides efficient and bias corrected estimates of the leading eigenvalues of \mathbf{Σ} under a spiked covariance model.

Usage

eigen.est(l, l.0, rho, K, n)

Arguments

l	eigenvalues of the sample covariance matrix
l.0	an estimate of noise via maximum likelihood
rho	the ratio n/(mw-1) where mw is the sample size
K	the number of spikes
n	the dimension of the covariance matrix

Details

This function is called by rmt.est and the estimate of noise, l.0, that is used here is \ell_0=(n-K)^{-1}∑_{j=K+1}^{n}\ell_j.

Value

1. l0.hat - bias corrected estimate of the unknown noise level

2. l.hat - bias corrected estimates of the leading K eignevalues of \mathbf{Σ}

References

1. Debashis Paul. Asymptotics of sample eigenstructure for a large dimensional spiked covariance model. Statistica Sinica, pages 1617-1642, 2007.

2. Alexei Onatski. Asymptotics of the principal components estimator of large factor models with weakly influential factors. Journal of Econometrics, 168(2):244-258, 2012.

3. Damien Passemier, Zhaoyuan Li, and Jianfeng Yao. On estimation of the noise variance in high dimensional probabilistic principal component analysis. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 79(1):51-67, 2017.

See Also

rmt.est

Examples

library(casp)
K = 4
n = 10
l = c(10,8,6,4,rep(1,6))
l.0 = ((n-K)^{-1})*sum(l[(K+1):n])
mw = 100
rho = n/(mw-1)
eigen.est(l,l.0,rho,K,n)

trambakbanerjee/casp documentation built on Nov. 22, 2022, 7:24 p.m.