Single functional index quantile regression under general dependence structure

Abstract

The main purpose of this paper is to estimate, semi-parametrically, the quantiles of a conditional distribution when the response is a real-valued random variable subject to a right-censorship phenomenon and the predictor takes values in an infinite dimensional space. We assume that the explanatory and the response variables are linked through a single-index structure. First, we introduce a kernel-type estimator of the conditional quantile when the data are supposed to be selected from an underlying stationary and ergodic process. Then, under some general conditions, the uniform almost-complete convergence rate as well as the asymptotic distribution of the estimator are established. A numerical study, including simulated and real data application, is performed to illustrate the validity and the finite-sample performance of the considered estimator.

Keywords:

• Conditional quantiles
• functional single-index model
• kernel estimator
• ergodic data

2010 Mathematics Subject Classifications:

• 62G20
• 62G05
• 62M10

Acknowledgements

The authors are grateful to two anonymous referees and Associate Editor that their careful reading gave them the opportunity to improve the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.