On a distribution-free quantile estimator ?
A distribution free non-kernel quantile estimator HDp 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 HDp(lc) which is a weighted version of HDp. The exact efficiency and simulation efficiency of HDp(lc) relative to the HDp 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.
level crossing empirical distribution function efficiency l estimators order statistics