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The Risk Inflation Criterion for Multiple Regression

Dean P. Foster and Edward I. George
The Annals of Statistics
Vol. 22, No. 4 (Dec., 1994), pp. 1947-1975
Stable URL: http://www.jstor.org/stable/2242493
Page Count: 29
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The Risk Inflation Criterion for Multiple Regression
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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 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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