A geometric interpretation of Mallows' C-p statistic and an alternative plot in variable selection


Siniksaran E.

COMPUTATIONAL STATISTICS & DATA ANALYSIS, vol.52, no.7, pp.3459-3467, 2008 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 52 Issue: 7
  • Publication Date: 2008
  • Doi Number: 10.1016/j.csda.2007.10.023
  • Journal Name: COMPUTATIONAL STATISTICS & DATA ANALYSIS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.3459-3467

Abstract

Mallows' C-p plot is a useful tool for variable selection in linear regression. Though not as popular as the C-p plot, Spjotvoll's F-p and P-p plots are also used in the variable selection procedure. The C-p, F-p and P-p 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 C-p or F-p plot is used. If a formal testing procedure is to be performed, then a P-p 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. (c) 2007 Elsevier B.V. All rights reserved.