Maximum Likelihood Shrinkage using Generalized Ridge or Least
Angle Regression
Description
Functions are provided to calculate and display ridge TRACE Diagnostics for a
variety of alternative Shrinkage Paths. While all methods focus on Maximum Likelihood
estimation of unknown true effects under normal distribution-theory, some estimates are
modified to be Unbiased or to have "Correct Range" when estimating either [1] the noncentrality
of the F-ratio for testing that true Beta coefficients are Zeros or [2] the "relative" MSE
Risk (i.e. MSE divided by true sigma-square, where the "relative" variance of OLS is known.)
The eff.ridge() function implements the "Efficient Shrinkage Path" introduced in Obenchain
(2022) . This "p-Parameter" Shrinkage-Path always passes through the
vector of regression coefficient estimates Most-Likely to achieve the overall Optimal
Variance-Bias Trade-Off and is the shortest Path with this property. Functions eff.aug() and
eff.biv() augment the calculations made by eff.ridge() to provide plots of the bivariate
confidence ellipses corresponding to any of the p*(p-1) possible ordered pairs of shrunken
regression coefficients. Functions for plotting TRACE Diagnostics now have more options.