Extremiles provide a generalization of quantiles which are not only robust, but also have an intrinsic link with extreme value theory. This paper introduces an extremile regression model tailored for functional covariate spaces. The estimation procedure turns out to be a weighted version of local linear scalar-on-function regression, where now a double kernel approach plays a crucial role. Asymptotic expressions for the bias and variance are established, applicable to both decreasing bandwidth sequences and automatically selected bandwidths. The methodology is then investigated in detail through a simulation study. Furthermore, we highlight the applicability of the model through the analysis of data sourced from the CH2018 Swiss climate scenarios project, offering insights into its ability to serve as a modern tool to quantify climate behaviour.

翻译：极端分位数不仅提供了对分位数概念的推广，具有稳健性，而且与极值理论存在内在联系。本文提出了一种专为函数型协变量空间设计的极端分位数回归模型。其估计过程可转化为加权版本的局部线性标量对函数回归，其中双核方法起着关键作用。研究建立了适用于递减带宽序列与自动选择带宽的偏差与方差渐近表达式，并通过模拟研究对该方法进行了详细验证。进一步地，我们通过分析CH2018瑞士气候情景项目的数据，展示了该模型的实际应用能力，论证了其作为量化气候行为的现代分析工具的有效性。