# Rank Verification for Exponential Families

arXiv: https://arxiv.org/abs/1610.03944 · HTML: https://mlsanity.com/paper/1610.03944/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2016.

## Built on by (most cited first, 13 of 13)

- [A Review of Adversarial Attack and Defense for Classification Methods](https://mlsanity.com/paper/2111.09961/) (2021)
- [Selective Ensembles for Consistent Predictions](https://mlsanity.com/paper/2111.08230/) (2021)
- [MedRDF: A Robust and Retrain-Less Diagnostic Framework for Medical Pretrained Models Against Adversarial Attack](https://mlsanity.com/paper/2111.14564/) (2021)
- [Invariance-Aware Randomized Smoothing Certificates](https://mlsanity.com/paper/2211.14207/) (2022)
- [Statistical Significance of Feature Importance Rankings](https://mlsanity.com/paper/2401.15800/) (2024)
- [Diffusion Denoised Smoothing for Certified and Adversarial Robust Out-Of-Distribution Detection](https://mlsanity.com/paper/2303.14961/) (2023)
- [Dynamic Defense Approach for Adversarial Robustness in Deep Neural Networks via Stochastic Ensemble Smoothed Model](https://mlsanity.com/paper/2105.02803/) (2021)
- [Locally minimax optimal confidence sets for the best model](https://mlsanity.com/paper/2503.21639/) (2025)
- [Powerful rank verification for multivariate Gaussian data with any covariance structure](https://mlsanity.com/paper/2503.01065/) (2025)
- [Integrating uncertainty quantification into randomized smoothing based robustness guarantees](https://mlsanity.com/paper/2410.20432/) (2024)
- [Boosting Adversarial Robustness using Feature Level Stochastic Smoothing](https://mlsanity.com/paper/2306.06462/) (2023)
- [Near Optimal Inference for the Best-Performing Algorithm](https://mlsanity.com/paper/2508.05173/) (2025)
- [How Sensitive Are LLM Leaderboard Claims to Hidden Model Selection?](https://mlsanity.com/paper/2609.28177/) (2026)

## Abstract (arXiv)

Many statistical experiments involve comparing multiple population groups. For example, a public opinion poll may ask which of several political candidates commands the most support; a social scientific survey may report the most common of several responses to a question; or, a clinical trial may compare binary patient outcomes under several treatment conditions to determine the most effective treatment. Having observed the "winner" (largest observed response) in a noisy experiment, it is natural to ask whether that candidate, survey response, or treatment is actually the "best" (stochastically largest response). This article concerns the problem of rank verification --- post hoc significance tests of whether the orderings discovered in the data reflect the population ranks. For exponential family models, we show under mild conditions that an unadjusted two-tailed pairwise test comparing the top two observations (i.e., comparing the "winner" to the "runner-up") is a valid test of whether the winner is truly the best. We extend our analysis to provide equally simple procedures to obtain lower confidence bounds on the gap between the winning population and the others, and to verify ranks beyond the first.