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

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

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

Description

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 Path has its single "interior" Knot at the Normal-theory Maximum Likelihood estimate with Minimum MSE Risk: d[j] = dMSE[j] for j = 1, 2, ..., p.

Usage

  meff(meobj, p, dMSE)

Arguments

meobj	A desired m-Extent of Shrinkage along the "efficient" Path.
p	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.
dMSE	Maximum Likelihood [ML] estimates of Shrinkage Delta-Factors leading to minimum MSE risk.

Value

The appropriate scalar value for m and corresponding p by p diagonal matrix d:

meobj	Any desired m-Extent of Shrinkage (a scalar) within [0, p].
d	The p by p diagonal matrix of shrinkage-factors: d[j,j] in [0, 1].

Author(s)

Bob Obenchain <[e-mail]>

See Also

eff.ridge and eff.aug.

RXshrink documentation built on Aug. 8, 2023, 1:09 a.m.