THE JOINT ASYMPTOTIC NORMALITY OF THE CONDITIONAL QUANTILES

Let (X, Y) be a two dimensional random variable with a joint distribution function F(x. y). This paper studies the kernel estimation of the conditional quantiles of Y for a given value of X based on a random sample from the above distribution, which was proposed by [12]. In this paper, the joint asymptotic normality of the conditional quantile estimated at a finite number of distinct points is established under some regularity conditions. Moreover, the performance of the conditional quantile estimation in constructing prediction intervals is tested through two applications. The first application deals with simulated data set and the second deals with real life data set.