SMOOTH NONPARAMETRIC-ESTIMATION OF THE QUANTILE FUNCTION

A smooth kernel estimator Rn(p) is proposed for nonparametric estimation of a population quantile ξp and its derivative ∂ξp ∂p. When the sample size n is large, the weights that Rn assigns to each order statistic are equivalent to the weights of the Qp statistic of Harrell and Davis (1982) and the Kp statistic of Kaigh and Lachenbruch (1982). The statistic Rn is a member of the class of estimators studied by Yang (1985) and uses a normal kernel function with a bandwidth proportional to{ p(1 - p) n} 1 2. A cross-validation technique is proposed for estimation of the smoothing parameter of Rn. Simulations indicate that the cross-validated Rn has a smaller mean squared error than Qp weighted over all values of p. © 1990.