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arXiv · 2510.10792

On function-on-function linear quantile regression

Muge Mutis·Ufuk Beyaztas·Filiz Karaman·Han Lin Shang
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Abstract

We present two innovative functional partial quantile regression algorithms designed to accurately and efficiently estimate the regression coefficient function within the function-on-function linear quantile regression model. Our algorithms utilize functional partial quantile regression decomposition to effectively project the infinite-dimensional response and predictor variables onto a finite-dimensional space. Within this framework, the partial quantile regression components are approximated using a basis expansion approach. Consequently, we approximate the infinite-dimensional function-on-function linear quantile regression model using a multivariate quantile regression model constructed from these partial quantile regression components. To evaluate the efficacy of our proposed techniques, we conduct a series of Monte Carlo experiments and analyze an empirical dataset, demonstrating superior performance compared to existing methods in finite-sample scenarios. Our techniques have been implemented in the ffpqr package in R.

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Muge Mutis, Ufuk Beyaztas, Filiz Karaman, Han Lin Shang. 2025-10-12. On function-on-function linear quantile regression. https://arxiv.org/abs/2510.10792

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