Abstract: | Let (X1, Y1), (X2, Y2), …, be two-dimensional random vectors which are independent and distributed as (X, Y). For 0<p<1, letξ(px) be the conditionalpth quantile ofYgivenX=x; that is,ξ(px)=inf{y : P(YyX=x)p}. We consider the problem of estimatingξ(px) from the data (X1, Y1), (X2, Y2), …, (Xn, Yn). In this paper, a new kernel estimator ofξ(px) is proposed. The asymptotic normality and a law of the iterated logarithm are obtained. |