RXshrink-internal

print.aug.lars

print.correct.signs

print.eff.ridge

print.MLboot

print.MLcalc

print.MLhist

print.MLtrue

print.qm.ridge

print.RXpredict

print.uc.lars

print.unr.ridge

print.eff.biv

print.YonX

mstep

kofm1

mofk1

mapp

These are internal functions for printing and calculating quantities such
 as additive K-factors and multiplicative Delta-Factors that determine a specified
 m-Extent of Shrinkage. mstep() is called by qm.ridge(), true.risk(), true.simu(), aug.lars()
 and uc.lars(). kofm1(), mofk1() and mapp() are called by YonX(). B19() is called by
 plot.eff.ridge() and plot.qm.ridge().

internal

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) <Open Statistics>. 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.

Bob Obenchain

RXshrink

Maximum Likelihood Shrinkage using Generalized Ridge or Least
Angle Regression

RXshrink-internal function

<dl> <dt>mobj</dt>
<dd>Objective value for the M-extent-of-shrinkage along a path of shape qp.</dd> <dt>kinc</dt>
<dd>Previous additive eigenvalue inflation constant yielding a smaller mobj.</dd> <dt>p</dt>
<dd>Number of estimates in the regression coefficient vector.</dd> <dt>qp</dt>
<dd>Shrinkage path Q-shape parameter.</dd> <dt>eqm1</dt>
<dd>Vector of X'X eigenvalues raised to the power (qp-1).</dd> <dt>k</dt>
<dd>Multiplicative factor that must decrease to increase shrinkage.</dd> <dt>dMSE</dt>
<dd>MSE Optimal Shrinkage delta-factor for YonX().</dd> <dt>muobj</dt>
<dd>Objective value for M-extent-of-shrinkage in kofm1().</dd> <dt>delmax</dt>
<dd>Scalar value strictly &lt; 1. Default value is delmax = 0.999999.</dd> <dt>mVal</dt>
<dd>Objective M-extent-of-shrinkage in mapp().</dd> <dt>YXobj</dt>
<dd>YonX object used by mapp().</dd> <dt>x</dt>
<dd>Numerical value argument for B19().</dd></dl>

Arguments

Bob Obenchain &lt;wizbob@att.net&gt;

Author

Internal RXshrink functions — RXshrink-internal

<dl>

 <dt>mobj</dt>
<dd>Objective value for the M-extent-of-shrinkage along a path of shape qp.</dd>

 <dt>kinc</dt>
<dd>Previous additive eigenvalue inflation constant yielding a smaller mobj.</dd>

 <dt>p</dt>
<dd>Number of estimates in the regression coefficient vector.</dd>

 <dt>qp</dt>
<dd>Shrinkage path Q-shape parameter.</dd>

 <dt>eqm1</dt>
<dd>Vector of X'X eigenvalues raised to the power (qp-1).</dd>

 <dt>k</dt>
<dd>Multiplicative factor that must decrease to increase shrinkage.</dd>

 <dt>dMSE</dt>
<dd>MSE Optimal Shrinkage delta-factor for YonX().</dd>

 <dt>muobj</dt>
<dd>Objective value for M-extent-of-shrinkage in kofm1().</dd>

 <dt>delmax</dt>
<dd>Scalar value strictly &lt; 1. Default value is delmax = 0.999999.</dd>

 <dt>mVal</dt>
<dd>Objective M-extent-of-shrinkage in mapp().</dd>

 <dt>YXobj</dt>
<dd>YonX object used by mapp().</dd>

 <dt>x</dt>
<dd>Numerical value argument for B19().</dd>

</dl>

Internal RXshrink functions

RXshrink-internal: Internal RXshrink functions

Description

Usage

Value

Arguments

Author