Statistics Papers

Document Type

Journal Article

Date of this Version

1994

Publication Source

The Annals of Statistics

Volume

22

Issue

4

Start Page

1947

Last Page

1975

DOI

10.1214/aos/1176325766

Abstract

A new criterion is proposed for the evaluation of variable selection procedures in multiple regression. This criterion, which we call the risk inflation, is based on an adjustment to the risk. Essentially, the risk inflation is the maximum increase in risk due to selecting rather than knowing the "correct" predictors. A new variable selection procedure is obtained which, in the case of orthogonal predictors, substantially improves on AIC, Cp and BIC and is close to optimal. In contrast to AIC, Cp and BIC which use dimensionality penalties of 2, 2 and logn, respectively, this new procedure uses a penalty 2logp, where p is the number of available predictors. For the case of nonorthogonal predictors, bounds for the optimal penalty are obtained.

Keywords

decision theory, minimax, model selection, multiple regression, risk, variable selection

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Date Posted: 27 November 2017

This document has been peer reviewed.