In this paper, we propose a model averaging approach for addressing model uncertainty in the context of partial linear functional additive models. These models are designed to describe the relation between a response and mixed-types of predictors by incorporating both the parametric effect of scalar variables and the additive effect of a functional variable. The proposed model averaging scheme assigns weights to candidate models based on the minimization of a multi-fold cross-validation criterion. Furthermore, we establish the asymptotic optimality of the resulting estimator in terms of achieving the lowest possible square prediction error loss under model misspecification. Extensive simulation studies and an application to a near infrared spectra dataset are presented to support and illustrate our method.

翻译：本文提出了一种模型平均方法，以解决部分线性函数加性模型中的模型不确定性问题。该类模型通过结合标量变量的参数效应和函数变量的加性效应，描述了响应变量与混合类型预测变量之间的关系。所提出的模型平均方案基于最小化多重交叉验证准则来为候选模型分配权重。此外，我们证明了在模型误设情况下，该方法所得到的估计量在实现最低平方预测误差损失方面具有渐近最优性。通过广泛的模拟研究以及对近红外光谱数据集的应用，我们进一步验证并展示了所提方法的有效性。