Extremile scalar-on-function regression

TL;DR

This paper introduces a novel extremile regression model for functional data, extending quantile concepts to extreme value analysis with robust estimation and practical applicability demonstrated through simulations and real data.

Contribution

It develops a new extremile regression approach for functional covariates using a double kernel local linear method, with theoretical bias-variance analysis.

Findings

Effective in capturing extreme behavior in functional data

Demonstrates good performance in simulations

Shows practical utility on Berkeley Growth data

Abstract

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 illustrate the method's applicability with an analysis of the Berkeley Growth data, showcasing its performance in a real-world functional data setting.