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.

中文翻译：

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功能性单指标分位数回归模型

众所周知，当目标是使用函数值协变量预测标量响应时，功能性单指标回归模型可以比功能性线性模型或完全非参数模型获得更好的预测精度。但是，这些模型的性能可能会因响应中的值过大或偏斜而受到不利影响。此外，他们无法提供响应的条件分布的全貌。通过使用上一天的\（\ hbox {PM} _ {{10}} \）浓度的轨迹来预测最大\（\ hbox {PM} _ {{10}} \}为了解决当前问题，提出了功能性单指数分位数回归模型。采用通用的剖析方法来估计模型。进行了仿真研究，以研究拟议估计量的有限样本性能。我们基于先前的日内\（\ hbox {PM} _ {{10}} \）浓度，运用建议的框架预测\（\ hbox {PM} _ {{10}} \）浓度的最大值天。