  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.
