Model Averaging by Cross-validation for Partially Linear Functional Additive Models

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.