Gaussian Rank Verification

Jeremy Goldwasser; Will Fithian; Giles Hooker

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arXiv · 2501.14142

Gaussian Rank Verification

Jeremy Goldwasser·Will Fithian·Giles Hooker

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Abstract

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.

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Jeremy Goldwasser, Will Fithian, Giles Hooker. 2025-01-23. Gaussian Rank Verification. https://arxiv.org/abs/2501.14142

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