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

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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

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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