Reproducing kernel‐based functional linear expectile regression

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