ASYMPTOTIC NORMALITY OF THE KERNEL ESTIMATOR OF CONDITIONAL QUANTILES IN A NORMED SPACE

M’hamed Ezzahrioui (France) and Elias Ould-Saïd (France)

Received April 6, 2007

Abstract

In this paper we study the problem of the estimation of the conditional quantile function when the covariables take values in some abstract function space. It is shown that, under some regularity conditions, the kernel estimate of the conditional quantile is asymptotically normally distributed. From this, we derive the asymptotic normality of a predictor and propose confidence bands for the conditional quantile function. Some simulations have been drawn to show how good the asymptotic normality is for finite samples.

Keywords and phrases: asymptotic normality, conditional distribution function, kernel estimator, functional data, small balls probability.