CovEst.hardPD: Covariance Estimation via Hard Thresholding under...

In CovTools: Statistical Tools for Covariance Analysis

Description

Sparse covariance estimation does not necessarily guarantee positive definiteness of an estimated covariance matrix. Fan et al. (2013) proposed to solve this issue by taking an iterative procedure to take an incremental decrease of threshold value until positive definiteness is preserved.

Usage

CovEst.hardPD(X)

Arguments

X	an (n\times p) matrix where each row is an observation.

Value

a named list containing:

S

a (p\times p) covariance matrix estimate.

optC

an optimal threshold value C_{min} that guarantees positive definiteness after thresholding.

References

\insertRef

fan_large_2013CovTools

Examples

## generate data from multivariate normal with Identity covariance.
pdim <- 5
data <- matrix(rnorm(10*pdim), ncol=pdim)

## apply 4 different schemes
out1 <- CovEst.hard(data, thr=0.1)  # threshold value 0.1
out2 <- CovEst.hard(data, thr=1)    # threshold value 1
out3 <- CovEst.hard(data, thr=10)   # threshold value 10
out4 <- CovEst.hardPD(data) # automatic threshold checking

## visualize 4 estimated matrices
mmessage <- paste("hardPD::optimal thr=",sprintf("%.2f",out4$optC),sep="")
gcol     <- gray((0:100)/100)
opar <- par(no.readonly=TRUE)
par(mfrow=c(2,2), pty="s")
image(out1$S[,pdim:1], col=gcol, main="thr=0.1")
image(out2$S[,pdim:1], col=gcol, main="thr=1")
image(out3$S[,pdim:1], col=gcol, main="thr=10")
image(out4$S[,pdim:1], col=gcol, main=mmessage)
par(opar)

CovTools documentation built on Aug. 14, 2021, 1:08 a.m.