shrinkcovmat

Provides nonparametric Steinian shrinkage estimators of the covariance matrix that are suitable in high dimensional settings, that is when the number of variables is larger than the sample size.

https://github.com/anestistouloumis/shrinkcovmat

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Provides nonparametric Steinian shrinkage estimators of the covariance matrix that are suitable in high dimensional settings, that is when the number of variables is larger than the sample size.

README.Rmd

---
output: rmarkdown::github_document
references:
- id: Touloumis2015
  title: Nonparametric Stein-type Shrinkage Covariance Matrix Estimators in High-Dimensional Settings
  author:
  - family: Touloumis
    given: Anestis
  container-title: Computational Statistics \& Data Analysis
  volume: 83
  URL: 'https://www.sciencedirect.com/science/article/pii/S0167947314003107'
  page: 251-261
  type: article-journal
  issued:
    year: 2015
csl: biometrics.csl    
---




```{r setup, include=FALSE}
knitr::opts_chunk$set(
  tidy = TRUE,
  collapse = TRUE,
  comment = "#>",
  fig.path = "README-")
```

# ShrinkCovMat: Shrinkage Covariance Matrix Estimators

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## Installation

You can install the release version of `ShrinkCovMat`:

```{r eval=FALSE}
install.packages("ShrinkCovMat")
```

The source code for the release version of `ShrinkCovMat` is available on CRAN at:

- https://CRAN.R-project.org/package=ShrinkCovMat

Or you can install the development version of `ShrinkCovMat`:

```{r eval=FALSE}
# install.packages('devtools')
devtools::install_github("AnestisTouloumis/ShrinkCovMat")
```

The source code for the development version of `ShrinkCovMat` is available on github at:

- https://github.com/AnestisTouloumis/ShrinkCovMat

To use `ShrinkCovMat`, you should first load the package as follows:

```{r}
library("ShrinkCovMat")
```

## Usage

This package provides estimates of the covariance matrix and in particular, it implements the nonparametric Stein-type shrinkage covariance matrix estimators proposed in @Touloumis2015. These estimators are suitable and statistically efficient regardless of the dimensionality.

Each of the three implemented shrinkage covariance matrix estimates is a convex linear combination of the sample covariance matrix and of a target matrix. The core function is called `shrinkcovmat` and the argument `target` defines one of the following three options for the target matrix: 

- the identity matrix (`target = "identity"`),
- the scaled identity matrix (`target = "spherical"`),
- the diagonal matrix with diagonal elements the corresponding sample variances (`target = "diagonal"`).

Calculation of the corresponding optimal shrinkage intensities is discussed in @Touloumis2015.

The utility function `targetselection` is designed to ease the selection of the target matrix. This is based on empirical observation by inspecting the estimated optimal intensities and the range and average of the sample variances.


## Example
Consider the colon cancer data example analyzed in @Touloumis2015. The data consists of two tissue groups: the normal tissue group and the tumor tissue group.
```{r}
data(colon)
normal_group <- colon[, 1:40]
tumor_group <- colon[, 41:62]
```
To decide the target matrix for covariance matrix of the normal group, inspect the following output:
```{r}
targetselection(normal_group)
```
The estimated optimal shrinkage intensity for the spherical matrix is slightly larger than the other two. In addition the sample variances appear to be of similar magnitude and their average is smaller than 1. Thus, the spherical matrix seems to be the most appropriate target for the covariance matrix. The resulting covariance matrix estimate is:
```{r}
estimated_covariance_normal <- shrinkcovmat(normal_group, target = "spherical")
estimated_covariance_normal
```
We follow a similar procedure for the tumor group: 
```{r}
targetselection(tumor_group)
```
As before, we may choose the spherical matrix as the target matrix. The resulting covariance matrix estimate for the tumor group is:
```{r}
estimated_covariance_tumor <- shrinkcovmat(tumor_group, target = "spherical")
estimated_covariance_tumor
```


## How to cite
```{r echo=FALSE, comment=NA}
citation("ShrinkCovMat")
```

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