GENERALIZED CROSS-VALIDATION AS A METHOD FOR CHOOSING A GOOD RIDGE PARAMETER
GENERALIZED CROSS-VALIDATION AS A METHOD FOR CHOOSING A GOOD RIDGE PARAMETER
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DOI：
10.1080/00401706.1979.10489751
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发表时间：
1979-01-01
期刊：
影响因子：
2.5
通讯作者：
WAHBA, G
中科院分区：
文献类型：
--
作者：
GOLUB, GH;HEATH, M;WAHBA, G
考虑模型未知时的岭估计(λ)，(β)=(λ+nλi)−1xTy。我们研究了从数据中选择较好的λ值的广义交叉验证方法。该估计是V(λ)的极小值，式中A(λ)=X(xTx+nλi)−1xT。这一估计是艾伦出版社的旋转不变版本，或普通的交叉验证。该估计值的作用类似于风险改善估计值，但不需要σ2的估计值，因此可以在n−pi较小时使用，甚至在某些情况下使用IFp≥2n。GCV方法也可以用于回归的子集选择和奇异值截断方法，甚至可以在这些方法的混合中进行选择。
Consider the ridge estimate (λ) for β in the model unknown, (λ) = (XTX+nλI)−1XTy. We study the method of generalized cross-validation (GCV) for choosing a good value for λ from the data. The estimate is the minimizer ofV(λ) given bywhereA(λ) =X(XTX+nλI)−1XT. This estimate is a rotation-invariant version of Allen's PRESS, or ordinary cross-validation. This estimate behaves like a risk improvement estimator, but does not require an estimate of σ2, so can be used whenn−pis small, or even ifp≥ 2nin certain cases. The GCV method can also be used in subset selection and singular value truncation methods for regression, and even to choose from among mixtures of these methods.