Partial Functioal Linear Model Based on RKHS and Ensemble Learning

Abstract

A new partial functional linear model is proposed for functional and vector-valued covariates with a scalar response. The proposed model assumes a linear relationship between the functional predictors and the scalar response, which is approximately estimated using a functional principal component basis expansion. For the vector-valued covariates, the flexibility of the model is enhanced by assuming that the connection function with the scalar response resides in a Reproducing Kernel Hilbert Space (RKHS), enabling its representation through a kernel function expansion. Furthermore, instead of relying on model selection, a ensemble learning approach is employed. By constructing partial functional linear models with different truncation numbers and performing a weighted average, the issue of truncation number selection is effectively addressed. Simulation studies and real data analysis demonstrate that the proposed method exhibits superior performance and competitiveness compared to the benchmark models.