We consider averaging a number of candidate models to produce a prediction of lower risk in the context of partially linear functional additive models. These models incorporate the parametric effect of scalar variables and the additive effect of a functional variable to describe the relationship between a response variable and regressors. We develop a model averaging scheme that assigns the weights by minimizing a cross-validation criterion. Under the framework of model misspecification, the resulting estimator is proved to be asymptotically optimal in terms of the lowest possible square error loss for prediction. Also, simulation studies and real data analysis demonstrate the good performance of our proposed method.

翻译：我们考虑在部分线性功能添加模型中平均使用一些候选模型来预测较低风险,这些模型包括卡路里变量的参数效应和功能变量的添加效应,以描述响应变量和递减变量之间的关系;我们制定平均模型,通过尽量减少交叉校验标准来分配加权数;在模型误判框架下,由此得出的估计值在预测中尽可能最低的平方差损失方面被证明是最佳的;此外,模拟研究和真实数据分析也显示了我们拟议方法的良好表现。