Partially linear functional quantile regression in a reproducing kernel Hilbert space

Abstract

We consider quantile functional regression with a functional part and a scalar linear part. We establish the optimal prediction rate for the model under mild assumptions in the reproducing kernel Hilbert space (RKHS) framework. Under stronger assumptions related to the capacity of the RKHS, the non-functional linear part is shown to have asymptotic normality. The estimators are illustrated in simulation studies.

Keywords:

• Convergence rate
• prediction risk
• quantile regression
• rademacher complexity

2020 Mathematics Subject Classification:

• 62G06

Acknowledgments

The authors sincerely thank the Editor Professor Ricardo Cao, the Associate Editor, and two anonymous reviewer for their insightful comments that have significantly improved this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Yan Zhou's research was supported by the National Natural Science Foundation of China (Grant No. 12071305, 11871390 and 11871411).