rmt.est: Estimation of leading eigenvalues and adjustment factors for...

In trambakbanerjee/casp: Coordinate-wise Adaptive Shrinkage Prediction

Estimation of leading eigenvalues and adjustment factors for the sample eigenvectors

Description

Provides (1) efficient and bias corrected estimates of the leading eigenvalues of \mathbf{Sigma} under a spiked covariance model, and (2) asymptotic adjustment factors for the sample eigenvectors.

Usage

rmt.est(K, S, mw)

Arguments

K	the number of spikes
S	the sample covariance matrix
mw	sample size

Details

This function is called by casp.checkloss, casp.linexloss and their counterparts for aggregated prediction.

Value

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

2. l.hat - bias corrected estimates of the leading K eignevalues of Sigma

3. pj - sample eigenvectors of \mathbf{S}

4. zeta - asymptotic adjustment factors for the eigenvectors of S

5. K - the number of spikes (provided as an input)

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

eigen.est, casp.checkloss, casp.linexloss, casp.agg.checkloss, casp.agg.linexloss

Examples

library(casp)
K = 4
S = diag(c(10,8,6,4,rep(1,6)))
mw = 50
rmt.out<- rmt.est(K,S,mw)

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