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arXiv · 2111.11776

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

Andrey Akinshin
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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 trade-off 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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Andrey Akinshin. 2021-11-23. Trimmed Harrell-Davis quantile estimator based on the highest density interval of the given width. https://doi.org/10.1080/03610918.2022.2050396

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