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This function makes classical (rather than Bayesian) Normal distribution-theory calculations of the form proposed in Obenchain(1977). Instead of providing "new" confidence regions for estimable linear functions, Generalized Ridge Regression (GRR) can focus interest on estimates that are within traditional confidence intervals and regions but which deviate reasonably from the centroid of that interval or region.
eff.aug(efobj)An output list object of class "eff.aug"...
Number of regression predictor variables.
The lm() output object for the model fitted using eff.ridge().
The p by 3 matrix of GRR coefficients. Column 1 contains OLS estimates, the middle column gives optimally biased coefficient estimates corresponding to the "Interior Knot" on all p of the Two-Piece Linear Splines, and column 3 contains all zeros for the Shrinkage Terminus.
Three increasing measures of shrinkage "Extent". The first is 0 for the OLS (BLUE) estimate, the second is the Maximum Likelihood m-Extent of Shrinkage [PURPLE point], and the third is m = p for Shrinkage to beta = 0. This "shrinkage terminus" [BLACK point] is frequently outside of the eff.biv() plot frame ...allowing the ellipse to be as LARGE as possible.
Names of all variables actually used in the GRR model.
An output object of class "eff.ridge".
Bob Obenchain <wizbob@att.net>
Obenchain RL. (1977) Classical F-tests and Confidence Regions for Ridge Regression. Technometrics 19, 429-439. tools:::Rd_expr_doi("10.1080/00401706.1977.10489582")
Obenchain RL. (2021) The Efficient Shrinkage Path: Maximum Likelihood of Minimum MSE Risk. https://arxiv.org/abs/2103.05161
Obenchain RL. (2022) Efficient Generalized Ridge Regression. Open Statistics 3: 1-18. tools:::Rd_expr_doi("10.1515/stat-2022-0108")
Obenchain RL. (2022) RXshrink_in_R.PDF RXshrink package vignette-like document, Version 2.1. http://localcontrolstatistics.org
eff.ridge and meff