internal function

Internal RXshrink functions

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().

mstep(mobj, kinc, p, qp, eqm1)
  mofk1(k, dMSE)
  kofm1(muobj, dMSE, delmax)
  mapp(mVal, YXobj)
  B19(x)

Arguments

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

Returns

An output list consisting of two objects (k-factor & d-matrix): - kinc: New k-factor producing an m-Extent-of-shrinkage of mobj.

• d: A pxp diagonal matrix of multiplicative shrinkage delta-factors for the uncorrelated components of the regression coefficient vector. p = 1 in mofk1().

• m: m-Extent of Shrinkage output by mofk1() or mapp().

• kStar: New k-factor producing an m-Extent-of-shrinkage of muobj.

Author(s)

Bob Obenchain wizbob@att.net