The Annals of Statistics

The Risk Inflation Criterion for Multiple Regression

Dean P. Foster and Edward I. George

Full-text: Open access

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, $C_p$ and BIC and is close to optimal. In contrast to AIC, $C_p$ and BIC which use dimensionality penalties of 2, 2 and $\log n$, respectively, this new procedure uses a penalty $2 \log p$, where $p$ is the number of available predictors. For the case of nonorthogonal predictors, bounds for the optimal penalty are obtained.

Article information

Source
Ann. Statist. Volume 22, Number 4 (1994), 1947-1975.

Dates
First available: 11 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176325766

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176325766

Mathematical Reviews number (MathSciNet)
MR1329177

Zentralblatt MATH identifier
0829.62066

Subjects
Primary: 62C99: None of the above, but in this section
Secondary: 62J05: Linear regression 62C20: Minimax procedures

Keywords
Decision theory minimax model selection multiple regression risk variable selection

Citation

Foster, Dean P.; George, Edward I. The Risk Inflation Criterion for Multiple Regression. The Annals of Statistics 22 (1994), no. 4, 1947--1975. doi:10.1214/aos/1176325766. http://projecteuclid.org/euclid.aos/1176325766.


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