CLT for single functional index quantile regression under dependence structure

Abstract

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.

Asymptotic Normality Single Functional Index Quantile Regression Under Randomly Censored Data

“…In this section we consider simulated data studies to assess the finite sample performance of the proposed estimator and compare it to its competitor. To study the behavior of our conditional quantiles estimator, we consider in this part a comparison of our CFSIM (2.4) model(functional single index model with censored data) with that of CNPFDA (5.1) (censored nonparametric functional data analysis), for more details, we can refer be made tothe works ([32] or [33])and in the latter, knowing the distribution of the regression model(the distribution is known and usual), we look to the behavior of our estimator of the conditional distribution function with respect to this distribution.…”

Asymptotic properties of the estimator of the conditional distribution for associated functional data

“…Functional Statistics was published by Ferraty, Laksaci, and Vieu (2006), who obtained some properties in the case i.i.d. The study of statistical models for infinite-dimensional (functional) data has been the subject of several works in recent statistical literature; the reader can consult the studies by Akkal, Kadiri, and Rabhi (2021), Kadiri, Rabhi, Khardani, and Akkal (2021), and references therein. The recent result on nonparametric estimation was obtained by Hamri, Mekki, Rabhi, and Kadiri (2022), who introduced a kernel estimator of the conditional distribution function and proved some asymptotic properties (with rate) in various situations including censored and/or independent variables.…”