PARTIAL NONLINEAR FUNCTIONAL REGRESSION MODEL: AN APPROACH VIA REPRODUCING KERNEL AND ENSEMBLE LEARNING

This study proposes a Partial Nonlinear Functional Regression Model (PNFLR) specifically designed to handle complex datasets where the Continuous Scalar Response Variable depends on a mixture of Vector-valued Covariates and Functional Covariates. The structural heterogeneity of these predictors is addressed by assuming a hybrid relationship: the vector components follow a standard Linear Association, whereas the functional inputs exhibit a complex Nonlinear Association with the response. To rigorously model this non-linearity within a Reproducing Kernel Hilbert Space (RKHS), the methodology departs from traditional single-kernel methods often characterized by rigid selection bias. Instead, the framework implements Model Averaging through an Ensemble Learning paradigm to facilitate the Adaptive Selection of kernel functions, thereby enhancing model flexibility. To ensure numerical stability and effective Regularization, a Truncated Approximation strategy is utilized. This process involves projecting the high-dimensional functional data onto a finite subspace via Functional Principal Component Basis Expansion, effectively mitigating overfitting risks while retaining essential structural information. By integrating kernel theory with ensemble mechanics, the PNFLR framework bridges the gap between theoretical function estimation and practical predictive modeling. Empirical evaluations on the Tecator dataset confirm that the architecture articulated herein yields superior Generalization Performance and lower error variance compared to conventional benchmark models across various prediction tasks, demonstrating robustness in real-world analytical scenarios.