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

TL;DR

This paper introduces a new smooth density estimator that is consistent with the Harrell-Davis quantile estimator, addressing inconsistencies between traditional density and quantile estimators, and supports discrete-continuous mixtures.

Contribution

It proposes a novel density estimator that aligns with the Harrell-Davis quantile estimator and includes a jittering implementation for mixed distributions.

Findings

The estimator is consistent with Harrell-Davis quantiles.

Supports discrete-continuous mixture distributions.

Improves reliability of density and quantile estimation.

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.