meff

A desired m-Extent of Shrinkage along the "efficient" Path.

meobj

The integer number of non-constant x-variables used in defining the linear
 model being fitted to ill-conditioned (intercorrelated, confounded) data. Note that
 p must also be rank of the given X-matrix.

Maximum Likelihood [ML] estimates of Shrinkage Delta-Factors leading to
 minimum MSE risk.

dMSE

The meff() function computes the numerical Shrinkage delta-factors corresponding to any
 desired m-Extent of Shrinkage, meobj, along the "efficient" (shortest) Path used by
 eff.ridge(). This Two-Piece Linear-Spline Path has its single "interior" Knot at the
 Normal-theory Maximum Likelihood estimate of Optimal MSE Risk: d[j] = dMSE[j] for
 j = 1, 2, ..., p.

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.

meff: m-Extents of Shrinkage used in eff.ridge() Calculations.

Description

Usage

Arguments

Value

See Also