Reproducing kernel‐based functional linear expectile regression

Abstract

Expectile regression is a useful alternative to conditional mean and quantile regression for characterizing a conditional response distribution, especially when the distribution is asymmetric or when its tails are of interest. In this article, we propose a class of scalar‐on‐function linear expectile regression models where the functional slope parameter is assumed to reside in a reproducing kernel Hilbert space (RKHS). Our approach addresses numerous drawbacks to existing estimators based on functional principal components analysis (FPCA), which make implicit assumptions about RKHS eigenstructure. We show that our proposed estimator can achieve an optimal rate of convergence by establishing asymptotic minimax lower and upper bounds on the prediction error. Under this framework, we propose a flexible implementation based on the alternating direction method of multipliers algorithm. Simulation studies and an analysis of real‐world neuroimaging data validate our methodology and theoretical findings and, furthermore, suggest its superiority over FPCA‐based approaches in numerous settings.