kisungyou / covtools

Statistical Tools for Covariance Analysis

CovTools

Covariance is of universal prevalence across various disciplines within statistics. This package aims at providing a rich collection of geometric and statistical tools for a variety of inferences on covariance structures as well as its inverse called precision matrix. See the package help file by help("package-CovTools") in R console for the list of available functions.

Installation

You can install the released version of CovTools from CRAN with:

install.packages("CovTools")

or the development version from github:

## install.packages("devtools")
## library(devtools)
devtools::install_github("kisungyou/CovTools")

List of Available Methods

We offer various methods for covariance and symmetric positive-definite matrices. Below is the list of functions implemented in our package.

(0) Elementary Operations

function name	description
CovDist	computes pairwise distance for symmetric positive-definite matrices
CovMean	estimate mean/average covariance matrix

(1) Estimation : Covariance

function name	authors	description
CovEst.adaptive	Cai and Liu (2011)	adaptive thresholding
CovEst.hard	Bickel and Levina (2008)	hard thresholding
CovEst.hardPD	Fan et al. (2013)	hard thresholding under positive-definiteness constraint
CovEst.nearPD	Qi and Sun (2006)	nearest positive-definite matrix projection
CovEst.soft	Antoniadis and Fan (2001)	soft thresholding
CovEst.2003LW	Ledoit and Wolf (2003)	linear shrinkage estimation
CovEst.2010OAS	Chen et al. (2010)	oracle approximation shrinkage
CovEst.2010RBLW	Chen et al. (2010)	Rao-Blackwell Ledoit-Wolf estimation

(2) Estimation : Precision

function name	authors	description
PreEst.2014An	An et al. (2014)	banded precision estimation via bandwidth test
PreEst.2014Banerjee	Banerjee and Ghosal (2014)	Bayesian estimation of a banded precision matrix
PreEst.2017Lee	Lee and Lee (2017)	Bayesian estimation of a banded precision matrix
PreEst.glasso	Friedman et al. (2008)	graphical lasso

(3) Hypothesis Test : 1-sample

function name	authors	description
BCovTeset1.mxPBF	Lee et al. (2018)	Bayesian test using Maximum Pairwise Bayes Factor
CovTest1.2013Cai	Cai and Ma (2013)	Test by Cai and Ma
CovTest1.2014Srivastava	Srivastava et al. (2014)	Test by Srivastava, Yanagihara, and Kubokawa

(4) Hypothesis Test : 2-sample

function name	authors	description
CovTest2.2013Cai	Cai and Ma (2013)	Test by Cai and Ma

(5) Hypothesis Test : 1-sample Diagonal

function name	authors	description
BDiagTest1.mxPBF	Lee et al. (2018)	Bayesian Test using Maximum Pairwise Bayes Factor
DiagTest1.2011Cai	Cai and Jiang (2011)	Test by Cai and Jiang
DiagTest1.2015Lan	Lan et al. (2015)	Test by Lan, Luo, Tsai, Wang, and Yang

covtools's Issues

CovEst.hardPD does not give positive definite matrix?

CovEst.hardPD() does not give a matrix that is positive definite? See code below

I believe this comes from the second search, which searches within the "first non pd" (Cvec1[iter]) to the last "pd" (Cvec1[iter-1]). It starts from the lowest, and then see if it is non pd. So this will stop at the first value (first non pd), and hence returns a non-pd value!?

Solution is probably either to inverse the line: Cvec2 = seq(from=Cvec1[iter], to=Cvec1[iter-1], length.out=20), or to change the sign in the second if ((min(eigen(tmpS, only.values=TRUE)$values)) < sqrt(.Machine$double.eps)){ to stop at the first pd?

Thanks!

library(CovTools)

pdim <- 20
data <- matrix(rnorm(10*pdim), ncol=pdim)

out4 <- CovEst.hardPD(data) 
min(eigen(out4$S, only.values = TRUE)$values)
#> [1] -0.2785753

## verify with matrixcalc
matrixcalc::is.positive.definite(out4$S)
#> [1] FALSE

^{Created on 2021-05-05 by the reprex package (v2.0.0)}

thr1.multiple: feeding X instead of S to func_

Hi Kisung

I was looking at the code, trying to implement Cai and Zhang (2016) shrinkage method allowing NA values.

Looking at thr1.multiple(), I notice that it takes a new function func_*_givenS, which seems to involve rewriting code many times? What was the reason for this exactly? The additional problem is that the function I am writing requires X at each iteration, meaning a _givenS function cannot be written.

It looks like thr1.multiple_X() could actually store the training X instead of computing the training S (S1), still compute the test S (S2) as before, and then thr1.singlesum() would work using the direct functions?

Am I missing something there? Happy to send a pull request for that!

Thanks alot!

Suggested changes:
new: X_train <-array(0,c(n1,p,nCV))
Change S1[,,i] = X[idx1,] into X_train[,,i] = X[idx1,,drop=FALSE]