# Gaussian Rank Verification

arXiv: https://arxiv.org/abs/2501.14142 · HTML: https://mlsanity.com/paper/2501.14142/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2025.

## Built on by (most cited first, 1 of 1)

- [Locally minimax optimal confidence sets for the best model](https://mlsanity.com/paper/2503.21639/) (2025)

## Abstract (arXiv)

Statistical experiments often seek to identify random variables with the largest population means. This inferential task, known as rank verification, has been well-studied on Gaussian data with equal variances. This work provides the first treatment of the unequal variances case, utilizing ideas from the selective inference literature. We design a hypothesis test that verifies the rank of the largest observed value without losing power due to multiple testing corrections. This test is subsequently extended for two procedures: Identifying some number of correctly-ordered Gaussian means, and validating the top-K set. The testing procedures are validated on NHANES survey data.