A kernel-type estimator for generalized quantiles

Abstract

Let HF be the distribution function of h(X1,…,Xm), where h is a real valued function of m variables and X1,…,Xn (n gt-or-equal, slanted m) is an i.i.d. sample from a distribution function F. A kernel-type estimator is proposed for the generalized quantile H−1F (p) (0 < p < 1). Under fairly general conditions we establish asymptotic normality of the estimator and consistent estimation of its asymptotic variance.