Asymptotic Results of a Nonparametric Conditional Quantile Estimator for Functional Time Series

ASYMPTOTIC NORMALITY SINGLE FUNCTIONAL INDEX QUANTILE REGRESSION UNDER RANDOMLY CENSORED DATA

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.

STRONG CONSISTENCY RATE OF THE CONDITIONAL QUANTILE ESTIMATOR WITH DATA MISSING AT RANDOM

In the case of response missing at random conditioned by a functional explanatory variable, this research investigates non parametric estimate of the conditional quantile using the kernel approach. Under an α-mixing assumption and properties of the small ball, we establish the uniform almost complete convergence (with rate) of the proposed estimator.