Abstract

Function-on-scalar regression models are extensively utilized in appli

cations involving longitudinal or functional responses. Prior literature has established the minimax optimal bounds for both mean and quantile regression.

This paper explores expectile regression as a natural extension to mean regression, particularly for modeling potential heteroscedasticity in data. We propose

an expectile function-on-scalar regression model that focuses on asymmetrical

regression of functional responses based on scalar predictors.

Employing the

structure of Reproducing Kernel Hilbert Space (RKHS), we have developed a

statistically efficient expectile estimator. This estimator comes with theoretical

backing, derived from the minimax rates of convergence in both random and fixed

design contexts. Our extensive simulations demonstrate the robust performance

of the proposed methods across various settings.

Additionally, we present an

empirical analysis using quality of life data from a breast cancer clinical trial,

showcasing the practical utility of our method.

Information

Preprint No.SS-2022-0206
Manuscript IDSS-2022-0206
Complete AuthorsYi Liu, Wei Tu, Yanchun Bao, Bei Jiang, Linglong Kong
Corresponding AuthorsLinglong Kong
Emailslkong@ualberta.ca

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Acknowledgments

Yi Liu is supported by the York University startup fund. Bei Jiang and

Linglong Kong were partially supported by grants from the Canada CIFAR

AI Chairs program, the Alberta Machine Intelligence Institute (AMII), and

Natural Sciences and Engineering Council of Canada (NSERC), and Linglong Kong was also partially supported by grants from the Canada Research

Chair program from NSERC.

Supplementary Materials

This supplemental material contains the technical proofs for Theorems 1–4.

Supplementary materials are available for download.