Function-on-function linear quantile regression

TL;DR

This paper introduces a flexible function-on-function linear quantile regression model that incorporates multiple functional predictors, uses functional principal component analysis, and employs Bayesian criteria for model selection, validated through simulations and real data.

Contribution

It presents a novel quantile regression framework for functional data with multiple predictors, including a Bayesian criterion for optimal component selection.

Findings

The proposed method performs well in simulations.

It effectively identifies significant predictors.

Provides accurate prediction intervals for response functions.

Abstract

In this study, we propose a function-on-function linear quantile regression model that allows for more than one functional predictor to establish a more flexible and robust approach. The proposed model is first transformed into a finite-dimensional space via the functional principal component analysis paradigm in the estimation phase. It is then approximated using the estimated functional principal component functions, and the estimated parameter of the quantile regression model is constructed based on the principal component scores. In addition, we propose a Bayesian information criterion to determine the optimum number of truncation constants used in the functional principal component decomposition. Moreover, a stepwise forward procedure and the Bayesian information criterion are used to determine the significant predictors for including in the model. We employ a nonparametric bootstrap procedure to construct prediction intervals for the response functions. The finite sample performance of the proposed method is evaluated via several Monte Carlo experiments and an empirical data example, and the results produced by the proposed method are compared with the ones from existing models.