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December, 1994 The Risk Inflation Criterion for Multiple Regression
Dean P. Foster, Edward I. George
Ann. Statist. 22(4): 1947-1975 (December, 1994). DOI: 10.1214/aos/1176325766


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.


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Dean P. Foster. Edward I. George. "The Risk Inflation Criterion for Multiple Regression." Ann. Statist. 22 (4) 1947 - 1975, December, 1994.


Published: December, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0829.62066
MathSciNet: MR1329177
Digital Object Identifier: 10.1214/aos/1176325766

Primary: 62C99
Secondary: 62C20 , 62J05

Keywords: decision theory , minimax , Model selection , multiple regression , risk , Variable selection

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.22 • No. 4 • December, 1994
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