A kernel estimator of a conditional quantile

Abstract

Let (X1, Y1), (X2, Y2), ..., be two-dimensional random vectors which are independent and distributed as (X, Y). For 0 < 1, let ξ(p | x) be the conditional pth quantile of Y given X = x; that is, ξ(p | x) = inf{ y : P(Y≤y | X = x)≥p}. We consider the problem of estimating ξ(p | x) from the data (X1, Y1), (X2, Y2), ..., (Xn, Yn). In this paper, a new kernel estimator of ξ(p | x) is proposed. The asymptotic normality and a law of the iterated logarithm are obtained. © 1996 Academic Press, Inc.