A new distribution-free quantile estimator

Abstract

A new distribution-free estimator Q p of the p th population quantile is formulated, where Q p is a linear combination of order statistics admitting a jackknife variance estimator having excellent properties. The small sample efficiency of Q p is studied under a variety of light and heavy-tailed symmetric and asymmetric distributions. For the distributions and values of p studied, Q p is generally substantially more efficient than the traditional estimator based on one or two order statistics.