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

## Adoption

## 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 tradeoff 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.

## Reference

Andrey Akinshin

“Trimmed Harrell-Davis quantile estimator based on the highest density interval of the given width”(2022) DOI: 10.1080/03610918.2022.2050396 arXiv:2111.11776

```
@Article{akinshin2022thdqe,
author = {Akinshin, Andrey},
title = {Trimmed Harrell-Davis quantile estimator based on the highest density interval of the given width},
journal = {Communications in Statistics - Simulation and Computation},
pages = {1-11},
year = {2022},
month = {3},
publisher = {Taylor & Francis},
doi = {10.1080/03610918.2022.2050396},
arxiv = {2111.11776},
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 tradeoff 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.}
}
```