A New Family of Nonparametric Quantile Estimators

Abstract

A new core methodology for creating nonparametric L-quantile estimators is introduced and three new quantile L-estimators (SV1 _p , SV2 _p , and SV3 _p ) are constructed using the new methodology. Monte Carlo simulation was used in order to investigate the performance of the new estimators for small and large samples under normal distribution and a variety of light and heavy-tailed symmetric and asymmetric distributions. The new estimators outperform, in most of the cases studied, the Harrell–Davis quantile estimator and the weighted average at X _([np]) quantile estimator.

Keywords:

• Estimators
• Nonparametric
• Order statistics
• Percentiles
• Quantiles

Mathematics Subject Classification:

• 62G05
• 62G30