solve_shrinking: Solve Linear Shrinking

In CovEsts: Nonparametric Estimators for Covariance Functions

Solve Linear Shrinking

Description

This is an objective function used to select \lambda \in [0, 1] in linear shrinking, see shrinking.

Usage

solve_shrinking(par, corr_mat, target)

Arguments

par	The initial parameter used in the maximisation process.
corr_mat	The autocorrelation matrix of the considered time series.
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.

Value

A numeric value that is either equal to -par or 1.

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, 0.5, 0)
corr_mat <- cyclic_matrix(estCorr)
solve_shrinking(0.5, corr_mat, diag(length(estCorr)))

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