ASYMPTOTIC NORMALITY SINGLE FUNCTIONAL INDEX QUANTILE REGRESSION UNDER RANDOMLY CENSORED DATA

Abstract

The main objective of this paper is to estimate non-parametrically the quantiles of a conditional distribution based on the single-index model in the censorship model when the sample is considered as an independent and identically distributed (i.i.d.) random variables. First of all, a kernel type estimator for the conditional cumulative distribution function (cond-cdf) is introduced. Afterwards, we give an estimation of the quantiles by inverting this estimated cond-cdf, the asymptotic properties are stated when the observations are linked with a single-index structure. Finally, a simulation study is carried out to evaluate the performance of this estimate.