岭回归是一种常用的用于克服多重共线性的压缩估计方法. 文章在存在异方差的背景下, 考察了组合不同岭参数下岭估计量的模型平均方法, 并在广义交叉核实法的框架下构造了相应的权重选择准则. 当拟合模型的设定存在偏误时, 证明了基于广义交叉核实法的模型平均法可以给出渐近最优的预测. 此外, 使用蒙特卡洛模拟考察了所提出的模型平均方法在有限样本下的有效性. 最终, 使用 所提出的方法对一组乙炔反应工艺的数据进行了分析, 所得到的结论进一步表明, 模型平均法在实际数据分析工作中具有较高应用价值.

Ridge regression is one of the most commonly used shrinkage methods for handling the problem of multicollinearity. In this paper, in the presence of heteroscedasticity, we consider the model averaging method for combining ridge estimators based on different ridge parameters. The corresponding weight choice method is proposed based on generalized cross validation. We show that when the fitting model is misspecified, the resulting model averaging estimator leads to the asymptotically optimal prediction. Monte-Carlo simulations are conducted to assess the effectiveness of the proposed method in finite sample setting. An application to the study concerning the acetylene process problem further supports the use of the model averaging method in practical situations.