Quantile-respectful density estimation based on the Harrell-Davis quantile estimator

The paper is based on a series of my research notes:

Quantile-respectful density estimation based on the Harrell-Davis quantile estimator (2020-10-27)
Improving quantile-respectful density estimation for discrete distributions using jittering (2021-04-27)
Quantile-Respectful Density Estimation and Trimming (2024-03-26)
Preprint announcement: 'Quantile-Respectful Density Estimation Based on the Harrell-Davis Quantile Estimator' (2024-04-09)

Abstract

Traditional density and quantile estimators are often inconsistent with each other. Their simultaneous usage may lead to inconsistent results. To address this issue, we propose a novel smooth density estimator that is naturally consistent with the Harrell-Davis quantile estimator. We also provide a jittering implementation to support discrete-continuous mixture distributions.

Reference

Andrey Akinshin “Quantile-respectful density estimation based on the Harrell-Davis quantile estimator” (2024) arXiv:2404.03835

@Article{akinshin2024qrdehd,
  title = {Quantile-respectful density estimation based on the Harrell-Davis quantile estimator},
  author = {Akinshin, Andrey},
  year = {2024},
  month = {4},
  day = {8},
  arxiv = {2404.03835},
  abstract = {Traditional density and quantile estimators are often inconsistent with each other. Their simultaneous usage may lead to inconsistent results. To address this issue, we propose a novel smooth density estimator that is naturally consistent with the Harrell-Davis quantile estimator. We also provide a jittering implementation to support discrete-continuous mixture distributions.}
}