THE RISK INFLATION CRITERION FOR MULTIPLE-REGRESSION
THE RISK INFLATION CRITERION FOR MULTIPLE-REGRESSION
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DOI：
10.1214/aos/1176325766
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发表时间：
1994-12-01
影响因子：
4.5
通讯作者：
GEORGE, EI
中科院分区：
文献类型：
--
作者：
FOSTER, DP;GEORGE, EI
提出了一种新的标准来评估多元回归中的变量选择程序。这个标准，我们称之为风险通胀，是基于对风险的调整。本质上，风险膨胀是由于选择而不是了解“正确”的预测因素而导致的风险的最大增加。获得了一种新的变量选择程序，在正交预测变量的情况下，该程序大大改进了 AIC、C-p 和 BIC，并且接近最优。与 AIC、C-p 和 BIC 分别使用 2、2 和 log n 的维度惩罚相比，这个新过程使用惩罚 2 log p，其中 p 是可用预测变量的数量。对于非正交预测变量的情况，获得最佳惩罚的界限。
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.