On a distribution-free quantile estimator

摘要

A distribution free non-kernel quantile estimator HD_p of the pth population quantile was introduced by Harrell and Davis (Biometrika 69(3) 1982) 635). In this paper, we use a level crossing empirical distribution function to propose a new estimator HD_(p(lc)) which is a weighted version of HD_p. The exact efficiency and simulation efficiency of HD_(p(lc)) relative to the HD_p quantile estimator are studied. From both the theoretical and computational points of view, the new estimator is more efficient in many cases, especially for the tails of the distributions and small sample sizes.