README.Rmd

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output: github_document
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# CovTools

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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.

## Installation

You can install the released version of CovTools from [CRAN](https://CRAN.R-project.org) with:

``` r
install.packages("CovTools")
```
or the development version from github:
```r
## 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 |