Extension of the harrell-davis quantile estimator to finite populations

Abstract

The quantile estimator formulated by Harrell and Davis (1982) as a linear combination of order statistics is extended to the case of sampling from a finite population. Sampling with and without replacement are considered. The relative efficiency of the estimator is discussed and then demonstrated with simulation evidence. A modified version of the estimator is discussed for the case of sampling without replacement. In the case of estimating the population median the proposed estimator is as much as 30% more efficient than the traditional sample median in the simulation experiments.

Keywords:

• finite population
• mean square error
• median
• order statistic
• quantile
• sampling without replacement