Extremile scalar‐on‐function regression

Abstract Extremiles provide a generalization of quantiles which are not only robust but also have an intrinsic link with extreme value theory. This article 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, which are applicable to both decreasing bandwidth sequences and automatically selected bandwidths. The methodology is then investigated in detail through a simulation study. Furthermore, we illustrate the method's applicability with an analysis of the Berkeley growth data, showcasing its performance in a real‐world functional data setting.