CLT for single functional index quantile regression under dependence structure

• Main Authors: Kadiri Nadia, Rabhi Abbes, Khardani Salah, Akkal Fatima
• Format: Article
• Language: English
• Published: Sciendo 2021-08-01
• Series: Acta Universitatis Sapientiae: Mathematica
• Subjects: conditional quantile; censored data; functional random variable; kernel estimator; nonparametric estimation; probabilities of small balls; strong mixing processes; single index model; primary 62g05; secondary 62g99; thirdly 62m10
• Online Access: https://doi.org/10.2478/ausm-2021-0003

In this paper, we investigate the asymptotic properties of a nonparametric conditional quantile estimation in the single functional index model for dependent functional data and censored at random responses are observed. First of all, we establish asymptotic properties for a conditional distribution estimator from which we derive an central limit theorem (CLT) of the conditional quantile estimator. Simulation study is also presented to illustrate the validity and finite sample performance of the considered estimator. Finally, the estimation of the functional index via the pseudo-maximum likelihood method is discussed, but not tackled.