shrinking: Linear Shrinking

In CovEsts: Nonparametric Estimators for Covariance Functions

Linear Shrinking

Description

This function corrects an autocovariance/autocorrelation function estimate via linear shrinking of the autocorrelation matrix.

Usage

shrinking(estCov, return_matrix = FALSE, target = NULL)

Arguments

estCov	A vector whose values are an estimate autocovariance/autocorrelation function.
return_matrix	A boolean determining whether the shrunken matrix or the corresponding vector is returned. If FALSE, it returns a vector whose values are the shrunken autocorrelation function. Defaults to FALSE.
target	A shrinkage target matrix used in the shrinking process. This should only be used if you wish to use a specific matrix as the target.

Details

This function corrects an autocovariance/autocorrelation function estimate via linear shrinking of the autocorrelation matrix. The shrunken autocorrelation matrix is computed as follows

\widetilde{R} = \lambda R + (1 - \lambda)I_{p},

where \widetilde{R} is the shrunken autocorrelation matrix, R is the original autocorrelation matrix, \lambda \in [0, 1], and I_{p} is the p\times p identity matrix. \lambda is chosen in such a away that largest value which still results in a positive-definite matrix. The shrunken matrix will be positive-definite.

Value

A vector with values of the shrunken autocorrelation function or the corresponding matrix (depending on return_matrix).

References

Devlin, S. J., Gnanadesikan R. & Kettenring, J. R. (1975). Robust Estimation and Outlier Detection with Correlation Coefficients. Biometrika, 62(3), 531-545. 10.1093/biomet/62.3.531

Rousseeuw, P. J. & Molenberghs, G. (1993). Transformation of Non Positive Semidefinite Correlation Matrices. Communications in Statistics - Theory and Methods, 22(4), 965–984. 10.1080/03610928308831068

Examples

estCorr <- c(1, 0.8, 0.5, -1.2)
shrinking(estCorr)
target <- diag(length(estCorr))
shrinking(estCorr, TRUE, target)

CovEsts documentation built on Sept. 10, 2025, 10:39 a.m.