Trimmed Harrell-Davis quantile estimator based on the highest density interval of the given width

TL;DR

This paper introduces a trimmed Harrell-Davis quantile estimator that balances efficiency and robustness by discarding low-weight order statistics based on the highest density interval of the beta distribution.

Contribution

It proposes a novel trimmed version of the Harrell-Davis estimator using the highest density interval to improve robustness while maintaining efficiency.

Findings

Enhanced robustness compared to the original Harrell-Davis estimator

Maintains high statistical efficiency for light-tailed distributions

Provides a customizable trade-off between robustness and efficiency

Abstract

Traditional quantile estimators that are based on one or two order statistics are a common way to estimate distribution quantiles based on the given samples. These estimators are robust, but their statistical efficiency is not always good enough. A more efficient alternative is the Harrell-Davis quantile estimator which uses a weighted sum of all order statistics. Whereas this approach provides more accurate estimations for the light-tailed distributions, it's not robust. To be able to customize the trade-off between statistical efficiency and robustness, we could consider a trimmed modification of the Harrell-Davis quantile estimator. In this approach, we discard order statistics with low weights according to the highest density interval of the beta distribution.