# Likelihood-ratio inference on differences in quantiles

DevFeed: [Likelihood-ratio inference on differences in quantiles](<https://devfeed.tech/articles/likelihood-ratio-inference-on-differences-in-quantiles-37878.md>)

Original publisher: [Read original article](<https://arxiv.org/abs/2401.10233>)

Author: Miller, Evan

Published: 2024-08-05T10:15:00Z

Content type: article

Language: en

Sources: [Evan Miller](<https://devfeed.tech/sources/evan-miller.md>)

Topics: [Statistics](<https://devfeed.tech/topics/statistics.md>), [Inference](<https://devfeed.tech/topics/inference.md>)

Tags: [confidence-interval](<https://devfeed.tech/tags/confidence-interval.md>), [experimentation](<https://devfeed.tech/tags/experimentation.md>), [statistics](<https://devfeed.tech/tags/statistics.md>)

## AI overview

This paper presents a two-sample hypothesis test and confidence interval for differences in quantiles using a likelihood-ratio test statistic. A conservative version avoids density estimation, while another version uses a density estimator and produces confidence intervals close to nominal coverage. The method can be computed from four order statistics from each sample.

## Source excerpt

Quantiles can represent key operational and business metrics, but the computational challenges associated with inference has hampered their adoption in online experimentation. In a new paper, I present a two-sample difference-in-quantile hypothesis test and confidence interval based on a likelihood-ratio test statistic. It can be computed using only four order statistics from each sample. arXiv link: Likelihood-ratio inference on differences in quantiles