普通交叉验证（OCV）和广义交叉验证（GCV）

Posted 2020-11-20 tango1221

普通交叉验证OCV

OCV是由Allen(1974)在回归背景下提出的，之后Wahba和Wold(1975)在讨论 了确定多项式回归中多项式次数的背景，在光滑样条背景下提出OCV。

 

 

Craven和Wahba（1979），Silverman（1985），Bates和其他人（1987），Wahba（1990）等人提出了所谓的GCV标准。

广义交叉验证的加权验证技术被用于协方差模型选择和参数估计。

The GCV funtion V(λ) is defined by :

 

具体详见（Spline models for observation data  的第四章介绍)

相关参考文献：

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