On function-on-function linear quantile regression - Mutis, Muge; Beyaztas, Ufuk; Karaman, Filiz; Shang, Han Lin (TAYLOR & FRANCIS LTD, 2025)
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 .
Keywords: Basis expansion functions; function-on-function linear quantile regression; functional partial least squares regression; quantile covariance; quantile regression; PRINCIPAL COMPONENT REGRESSION; Mathematics