THE RISK INFLATION CRITERION FOR MULTIPLE-REGRESSION

A new criterion is proposed for the evaluation of variable selection p rocedures in multiple regression. This criterion, which we call the ri sk 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 pro cedure is obtained which, in the case of orthogonal predictors, substa ntially improves on AIC, C-p and BIC and is close to optimal. In contr ast 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 nonorthogona l predictors, bounds for the optimal penalty are obtained.