Function-on-function linear quantile regression

Ufuk Beyaztas*, Han Lin Shang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
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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.
Original languageEnglish
Pages (from-to)322-341
Number of pages20
JournalMathematical Modelling and Analysis
Issue number2
Publication statusPublished - 27 Apr 2022

Bibliographical note

Copyright 2022 The Author(s). Published by Vilnius Gediminas Technical University. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


  • function-on-function regression
  • functional principal component analysis
  • median regression
  • quantile regression


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