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

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 unr.ridge() function implements the "Unrestricted Path" introduced in Obenchain (2020) <arXiv:2005.14291>. This "new" p-parameter Shrinkage-Path and that of eff.ridge() are both more efficient than the Paths used by qm.ridge(), aug.lars() and uc.lars(). 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 pairs of shrunken regression coefficients.

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