Functional single-index quantile regression models

It is known that functional single-index regression models can achieve better prediction accuracy than functional linear models or fully nonparametric models, when the target is to predict a scalar response using a function-valued covariate. However, the performance of these models may be adversely affected by extremely large values or skewness in the response. In addition, they are not able to offer a full picture of the conditional distribution of the response. Motivated by using trajectories of \(\hbox {PM}_{{10}}\) concentrations of last day to predict the maximum \(\hbox {PM}_{{10}}\) concentration of the current day, a functional single-index quantile regression model is proposed to address those issues. A generalized profiling method is employed to estimate the model. Simulation studies are conducted to investigate the finite sample performance of the proposed estimator. We apply the proposed framework to predict the maximal value of \(\hbox {PM}_{{10}}\) concentrations based on the intraday \(\hbox {PM}_{{10}}\) concentrations of the previous day.