**Update: the final paper was published in Communications in Statistics - Simulation and Computation (DOI: 10.1080/03610918.2022.2050396).**

Since the beginning of this year, I have been working on building a quantile estimator that provides an optimal trade-off between statistical efficiency and robustness. Finally, I have built such an estimator. A paper preprint is available on arXiv: arXiv:2111.11776 [stat.ME]. The paper source code is available on GitHub: AndreyAkinshin/paper-thdqe. You can cite it as follows:

- Andrey Akinshin (2021) Trimmed Harrell-Davis quantile estimator based on the highest density interval of the given width, arXiv:2111.11776

### Relevant blog posts

Here is the full list of relevant blog posts:

- Winsorized modification of the Harrell-Davis quantile estimator
*(March 2, 2021)* - Efficiency of the Harrell-Davis quantile estimator
*(March 23, 2021)* - Trimmed modification of the Harrell-Davis quantile estimator
*(March 30, 2021)* - Efficiency of the winsorized and trimmed Harrell-Davis quantile estimators
*(April 6, 2021)* - Improving the efficiency of the Harrell-Davis quantile estimator for special cases using custom winsorizing and trimming strategies
*(May 25, 2021)* - Optimal threshold of the trimmed Harrell-Davis quantile estimator
*(July 20, 2021)* - Avoiding over-trimming with the trimmed Harrell-Davis quantile estimator
*(July 27, 2021)* - Quantile estimators based on k order statistics, Part 1: Motivation
*(August 3, 2021)* - Quantile estimators based on k order statistics, Part 2: Extending Hyndman-Fan equations
*(August 10, 2021)* - Quantile estimators based on k order statistics, Part 3: Playing with the Beta function
*(August 17, 2021)* - Quantile estimators based on k order statistics, Part 4: Adopting trimmed Harrell-Davis quantile estimator
*(August 24, 2021)* - Quantile estimators based on k order statistics, Part 5: Improving trimmed Harrell-Davis quantile estimator
*(August 31, 2021)* - Quantile estimators based on k order statistics, Part 6: Continuous trimmed Harrell-Davis quantile estimator
*(September 7, 2021)* - Quantile estimators based on k order statistics, Part 7: Optimal threshold for the trimmed Harrell-Davis quantile estimator
*(September 14, 2021)* - Quantile estimators based on k order statistics, Part 8: Winsorized Harrell-Davis quantile estimator
*(September 21, 2021)* - Beta distribution highest density interval of the given width
*(September 28, 2021)* - Optimal window of the trimmed Harrell-Davis quantile estimator, Part 1: Problems with the rectangular window
*(October 5, 2021)* - Optimal window of the trimmed Harrell-Davis quantile estimator, Part 2: Trying Planck-taper window
*(October 12, 2021)* - Trimmed Harrell-Davis quantile estimator based on the highest density interval of the given width
*(October 19, 2021)* - Preprint announcement: 'Trimmed Harrell-Davis quantile estimator based on the highest density interval of the given width'
*(November 30, 2021)* - Publication announcement: 'Trimmed Harrell-Davis quantile estimator based on the highest density interval of the given width'
*(March 22, 2022)*

### BibTeX reference

```
@article{akinshin2021thdqe,
title={Trimmed Harrell-Davis quantile estimator based on the highest density interval of the given width},
author={Andrey Akinshin},
year={2021},
eprint={2111.11776},
archivePrefix={arXiv},
primaryClass={stat.ME},
url={https://arxiv.org/abs/2111.11776}
}
```