The TRACE display below shows how fitted regression coefficients for the infamous Longley(1967) dataset change due to shrinkage along a Q-shape = -1.5 path through 6-dimensional coefficient likelihood space.
Shrinkage methods can drastically reduce variability, but shrinkage also results in biased estimates. Since mean-squared-error risk is made up of variance plus squared-bias, shrinkage reduces risk whenever the unknown squared-bias introduced is less than the known reduction in (relative) variance.
To apply shrinkage methodology, the two key questions that a regression practitioner must answer are:
softRX freeware is proud to provide computer algorithms for R, XLisp-Stat, Stata, Gauss and SAS-IMSL to guide you along your shrinkage regression "journey" by providing powerful, maximum likelihood statistical inferences and dynamic graphical insights along the "route" of your choice! Related materials are...