# Shrinking the Sample Covariance Matrix Towards a Diagonal Matrix with Diagonal Elements the Sample Variances.

### Description

Provides a nonparametric Stein-type shrinkage estimator of the covariance matrix that is a linear combination of the sample covariance matrix and of the diagonal matrix with elements the corresponding sample variances on the diagonal and zeros elsewehere.

### Usage

1 | ```
shrinkcovmat.unequal(data, centered = FALSE)
``` |

### Arguments

`data` |
a numeric matrix containing the data. |

`centered` |
a logical indicating if the vectors are centered around their mean vector. |

### Details

The rows of the data matrix `data`

correspond to variables and the columns to subjects.

### Value

Returns an object of the class "shrinkcovmathat" that has components:

`Sigmahat` |
The Stein-type shrinkage estimator of the covariance matrix. |

`lambdahat` |
The estimated optimal shrinkage intensity. |

`Sigmasample` |
The sample covariance matrix. |

`Target` |
The target covariance matrix. |

`centered` |
If the data are centered around their mean vector. |

### Author(s)

Anestis Touloumis

### References

Touloumis, A. (2015) Nonparametric Stein-type Shrinkage Covariance Matrix Estimators in High-Dimensional Settings. *Computational Statistics & Data Analysis* **83**, 251–261.

### See Also

`shrinkcovmat.equal`

and `shrinkcovmat.identity`

.

### Examples

1 2 3 4 5 6 7 | ```
data(colon)
normal.group <- colon[, 1:40]
colon.group <- colon[, 41:62]
Sigmahat.normal <- shrinkcovmat.unequal(normal.group)
Sigmahat.normal
Sigmahat.colon <- shrinkcovmat.unequal(colon.group)
Sigmahat.colon
``` |