Papers / Trimmed Harrell-Davis Quantile Estimator Based on the Highest Density Interval of the Given Width

2022 Perfology / Statistics Projects / Statistical Performance Analysis Topics / Mathematics Topics / Statistics Authors / Andrey Akinshin
DOI: 10.1080/03610918.2022.2050396 arXiv:2111.11776 AndreyAkinshin/paper-thdqe

Reference

Andrey Akinshin “Trimmed Harrell-Davis quantile estimator based on the highest density interval of the given width” (2022) // Communications in Statistics - Simulation and Computation. Publisher: Taylor & Francis. Pp. 1-11. DOI: 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.

Bib

@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.}
}
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