Since the beginning of previous year, I have been working on building a quantile estimator that provides an optimal trade-off between statistical efficiency and robustness. At the end of the year, I published the corresponding preprint where I presented a description of such an estimator: arXiv:2111.11776 [stat.ME]. The paper source code is available on GitHub: AndreyAkinshin/paper-thdqe.

Finally, the paper was published in *Communications in Statistics - Simulation and Computation*.
You can cite it as follows:

- Andrey Akinshin (2022)
*Trimmed Harrell-Davis quantile estimator based on the highest density interval of the given width,*Communications in Statistics - Simulation and Computation, DOI: 10.1080/03610918.2022.2050396

Here is the corresponding BibTeX reference:

```
@article{akinshin2022thdqe,
author = {Andrey Akinshin},
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},
publisher = {Taylor & Francis},
doi = {10.1080/03610918.2022.2050396},
URL = {https://www.tandfonline.com/doi/abs/10.1080/03610918.2022.2050396},
eprint = {https://www.tandfonline.com/doi/pdf/10.1080/03610918.2022.2050396},
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.}
}
```

### 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)*