  Functional regression is very crucial in functional data analysis and a
linear relationship between scalar response and functional predictor is often
assumed. However, the linear assumption may not hold in practice, which makes
the methods for linear models invalid. To gain more flexibility, we focus on
functional nonlinear models and aim to develop new method that requires no
strict constraint on the nonlinear structure. Inspired by the idea of the
kernel method in machine learning, we propose a kernel functional partial least
squares (KFPLS) method for the functional nonlinear models. The innovative
algorithm works on the prediction of the scalar response and is accompanied by
R package KFPLS for implementation. The simulation study demonstrates the
effectiveness of the proposed method for various types of nonlinear models.
Moreover, the real world application also shows the superiority of the proposed
KFPLS method.
