A robust partial least squares approach for function-on-function regression

TL;DR

This paper introduces a robust estimation method for function-on-function linear regression that effectively handles outliers, improves prediction accuracy, and determines optimal components through a data-driven criterion, validated by simulations and real data.

Contribution

A novel robust partial least squares approach for function-on-function regression that enhances outlier resistance and prediction accuracy, with an automatic component selection procedure.

Findings

The proposed method outperforms existing techniques in simulations.

It provides more accurate predictions in the presence of outliers.

Bootstrap-based prediction intervals are effectively constructed.

Abstract

The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors. Existing methods to estimate the model parameters may be sensitive to outlying observations, common in empirical applications. In addition, these methods may be severely affected by such observations, leading to undesirable estimation and prediction results. A robust estimation method, based on iteratively reweighted simple partial least squares, is introduced to improve the prediction accuracy of the function-on-function linear regression model in the presence of outliers. The performance of the proposed method is based on the number of partial least squares components used to estimate the function-on-function linear regression model. Thus, the optimum number of components is determined via a data-driven error criterion. The finite-sample performance of the proposed method is investigated via several Monte Carlo experiments and an empirical data analysis. In addition, a nonparametric bootstrap method is applied to construct pointwise prediction intervals for the response function. The results are compared with some of the existing methods to illustrate the improvement potentially gained by the proposed method.