Functional Partial Linear Model

TL;DR

This paper introduces a semi-parametric model for scalar response prediction with functional explanatory variables, combining linear and complex relationships, and analyzes its theoretical properties and finite sample performance.

Contribution

It proposes a novel semi-parametric functional model that integrates parametric and nonparametric approaches, with established asymptotic properties.

Findings

Asymptotic properties of estimators are derived.

Finite sample behavior is validated through simulations.

The model effectively captures mixed relationships between variables.

Abstract

When predicting scalar responses in the situation where the explanatory variables are functions, it is sometimes the case that some functional variables are related to responses linearly while other variables have more complicated relationships with the responses. In this paper, we propose a new semi-parametric model to take advantage of both parametric and nonparametric functional modeling. Asymptotic properties of the proposed estimators are established and finite sample behavior is investigated through a small simulation experiment.