高维回归中基于组块3×2交叉验证的调节参数选择

Tuning Parameter Selection Based on Blocked 3×2 Cross-Validation in High Dimensional Regression

将组块3×2交叉验证方法用于高维回归中的调节参数选择.首先通过ISIS方法把模型的维数降低到样本个数以内,然后使用AENET方法对降维后的模型进行进一步的降维和参数估计,使用组块3×2交叉验证方法选择最佳的调节参数.综合考虑模拟实验中各种调节参数选择方法(AIC、BIC、EBIC、HBIC、5折交叉验证、组块3×2交叉验证)的EMSE值、方差以及计算复杂度,结果表明基于组块3×2交叉验证的方法是有其优势的.

In the traditional regression model,the fold cross-validation can identify the true model eter selection methods. However,these criterions information criterions （AIC,BIC） and standard K consistently as the commonly used tuning param- tend to fail when meeting high dimensional data. Recent research shows that the 2-fold cross-validation has some advantages on the computation complexity,model selection and comparisons of models performances,especially the blocked 3 ×2 cross-validation newly proposed in the literature. Thus,we apply the blocked 3×2 cross-validation to the tuning parameter selection in high dimensional regression. First,the model dimension is re- duced to a scale with smaller than sample size by ISIS method. Then, the dimension reduced model is further to be reduced dimention and estimated parameters by AENET. And the tuning parameter is selected by using the blocked 3×2 cross-validation. Taking all factors into considera- tion of the EMSE values,variance and computation complexity of various tuning parameter selec- tion methods （AIC,BIC,EBIC, HBIC,5-fold cross-validation and blocked 3 × 2 cross-validation） in simulated experiments,the blocked 3×2 cross-validation method is comparable.