普通交叉驗證(OCV)和廣義交叉驗證(GCV)


普通交叉驗證OCV

OCV是由Allen(1974)在回歸背景下提出的,之后Wahba和Wold(1975)在討論 了確定多項式回歸中多項式次數的背景,在光滑樣條背景下提出OCV。

 

 

Craven和Wahba(1979),Silverman(1985),Bates和其他人(1987),Wahba(1990)等人提出了所謂的GCV標准。

廣義交叉驗證的加權驗證技術被用於協方差模型選擇和參數估計。

The GCV funtion V(λ) is defined by :

 

具體詳見(Spline models for observation data  的第四章介紹)

相關參考文獻:

  1. Allen, David M. The Relationship Between Variable Selection and Data Agumentation and a Method for Prediction. Technometrics, Vol. 16, No. 1 (February, 1974), pp. 125-127

  2. Craven, Peter and Wahba, Grace. Smoothing Noisy Data with Spline Functions. Numerische Mathematik 31, (1979), pp. 377-403

  3. Efron, Bradley. How Biased Is the Apparent Error Rate of a Logistic Regression? Technical report no. 232. Department of Statistics, Stanford University (April 1985)

  4. Golub, Gene H., Heath and Grace Wahba. Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter. Technometrics, Vol. 21, No. 2 (May, 1979), pp. 215-223

 


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