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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.


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


or the development version from github:

## install.packages("devtools")
## library(devtools)

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