/ January 1997/ version 3.0 /
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 variance.
To apply shrinkage methodology, the two key questions that a regression practitioner must answer are:
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