RXshrink: Maximum Likelihood Shrinkage using Generalized Ridge or Least Angle Regression

Functions are provided to calculate and display ridge TRACE diagnostics for a wide 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 (2021) <arXiv:2103.05161>. This new "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.

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