Description
Statistical Tools for Covariance Analysis.
Description
Covariance is of universal prevalence across various disciplines within statistics. We provide a rich collection of geometric and inferential tools for convenient analysis of covariance structures, topics including distance measures, mean covariance estimator, covariance hypothesis test for one-sample and two-sample cases, and covariance estimation. For an introduction to covariance in multivariate statistical analysis, see Schervish (1987) <doi:10.1214/ss/1177013111>.
README.md
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. |