On function-on-function linear quantile regression

Mutiş M., Beyaztaş U., Karaman F., Shang H. L.

JOURNAL OF APPLIED STATISTICS, vol.52, no.4, pp.814-840, 2025 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 52 Issue: 4
  • Publication Date: 2025
  • Doi Number: 10.1080/02664763.2024.2395960
  • Journal Name: JOURNAL OF APPLIED STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, Aerospace Database, Applied Science & Technology Source, Business Source Elite, Business Source Premier, CAB Abstracts, Computer & Applied Sciences, Veterinary Science Database, zbMATH
  • Page Numbers: pp.814-840
  • Yıldız Technical University Affiliated: Yes

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.