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}
}