A geometric interpretation of Mallows’ Cp statistic and an alternative plot in variable selection

摘要

Mallows’ Cp plot is a useful tool for variable selection in linear regression. Though not as popular as the Cp plot, Spjotvoll’s Fp and Pp plots are also used in the variable selection procedure. The Cp, Fp and Pp plots are useful in their own right. If the interest is the direct measure of the amount of bias of the submodels and a distributional assumption is not made about the error term, a Cp or Fp plot is used. If a formal testing procedure is to be performed, then a Pp plot is employed. A geometrical approach is used in order to propose an alternative plot that unifies all the information in these three plots, and that has some advantages over them. A Mathematica package has been written to implement the approach.