ShrinkCovMat (version 1.0.0)

shrinkcovmat.equal: Shrinking the Sample Covariance Matrix Towards a Diagonal Matrix with Equal Elements

Description

This function provides a nonparametric Stein-type shrinkage estimator of the covariance matrix that is a linear combination of the sample covariance matrix and of a diagonal matrix with elements the average of the diagonal elements of the sample covariance matrix.

Usage

shrinkcovmat.equal(data, centered = FALSE)

Arguments

data

a numeric matrix containing the data.

centered

a logical indicating if the mean vector is the zero vector.

Value

• Returns an object of the class "covmat" that has components:
• Sigmahat
  The Stein-type shrinkage estimator of the covariance matrix.
• lambdahat
  The estimated optimal shrinkage intensity.
• Sigmasam
  The sample covariance matrix.
• Target
  The target covariance matrix.
• centered
  If the data are centered around their mean vector.

Details

The rows of the data matrix data correspond to the variables and the columns to different subjects.

References

Touloumis, A. (2014). Nonparametric Stein-type shrinkage covariance matrix estimators in high-dimensional settings. Submitted.

See Also

shrinkcovmat.unequal and shrinkcovmat.identity.

Examples

data(colon)
normal.group <- colon[,1:40]
colon.group <- colon[,41:62]
Sigma.normal <- shrinkcovmat.equal(normal.group)
Sigma.normal
Sigma.colon <- shrinkcovmat.equal(colon.group)
Sigma.colon