Partial functional linear regression based on the Stacking and RKHS

Functional regression models represent a crucial research area within functional data analysis. To enhance the flexibility of the model, this paper proposes a partial functional linear regression model based on ensemble learning and kernel techniques. On one hand, this method effectively models the relationship between non-linear predictor variables and scalar response variables by employing the Reproducing Kernel Hilbert Space. On the other hand, it utilizes Functional Principal Component Analysis to approximate and estimate functional predictor variables, and addresses the selection of truncation numbers through the stacking framework. In the stacking framework, the meta model takes a model-free form, further increasing the flexibility of the model and effectively balancing the variance and bias of the prediction model. The results of simulation experiments and real-world data analysis demonstrate that the proposed method is more competitive compared to traditional benchmark methods.