mofk

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.

The given k-factor that multiplies each given dMSE-factor.

Maximum Likelihood estimates of Shrinkage Delta-Factors with minimum MSE risk.

dMSE

The mofk() function computes the numerical m-Extent of Shrinkage corresponding to a given
 value for "k", the scalar that multiplies observed ML estimates of "dMSE"-factors for
 each of the "p" uncorrelated components in GRR estimation using unr.ridge(). These
 calculations are quite simple; the function is many-to-one in the sense that all truly
 large values of k imply that m = 0.0, and k values that are either 0.0 or negative imply
 that m = p.

regression

Functions are provided to calculate and display ridge TRACE diagnostics for
a variety of shrinkage Paths. TRACEs identify the m-Extent of shrinkage most likely,
under Normal-theory, to produce optimally biased estimates of beta-coefficients with
minimum MSE Risk. The unr.ridge() function implements the "Unrestricted Path"
introduced in Obenchain (2020) <arXiv:2005.14291>. This Shrinkage-Path is more
efficient than the Paths used by the qm.ridge(), aug.lars() and uc.lars() functions.
Optimally biased predictions can be made using RXpredict() for all six types of
RXshrink linear model estimation methods. Functions MLboot(), MLcalc(), MLhist() and
MLtrue() provide insights into the true bias and MSE risk characteristics of non-linear
Shrinkage estimators. Functions unr.aug() and unr.biv() augment the calculations made
by unr.ridge() to provide plots of the bivariate confidence ellipses corresponding to
any of the p*(p-1) possible pairs of shrunken regression coefficients. The correct.signs()
function provides estimates with "correct" numerical signs when ill-conditioned (nearly
multicollinear) models yield OLS estimates that disagree with the signs of the observed
correlations between the y-outcome and the selected x-predictor variables.

mofk: m-Extents of Shrinkage used in unr.ridge() Calculations.

Description

Usage

Arguments

Value

References

See Also