Model Averaging by Cross-validation for Partially Linear Functional Additive Models

TL;DR

This paper introduces a model averaging method using cross-validation for partially linear functional additive models, effectively handling model uncertainty and improving prediction accuracy in complex data settings.

Contribution

It proposes a novel cross-validation based model averaging scheme for partially linear functional additive models, with proven asymptotic optimality.

Findings

The method achieves lower prediction error in simulations.

It successfully models complex relationships in real data.

The approach outperforms existing methods in predictive accuracy.

Abstract

In this paper, we propose a model averaging approach for addressing model uncertainty in the context of partial linear functional additive models. These models are designed to describe the relation between a response and mixed-types of predictors by incorporating both the parametric effect of scalar variables and the additive effect of a functional variable. The proposed model averaging scheme assigns weights to candidate models based on the minimization of a multi-fold cross-validation criterion. Furthermore, we establish the asymptotic optimality of the resulting estimator in terms of achieving the lowest possible square prediction error loss under model misspecification. Extensive simulation studies and an application to a near infrared spectra dataset are presented to support and illustrate our method.