# Hypothesis Testing for High-Dimensional Multinomials: A Selective Review

arXiv: https://arxiv.org/abs/1712.06120 · HTML: https://mlsanity.com/paper/1712.06120/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Dec 2017.

## Built on by (most cited first, 8 of 8)

- [T-Cal: An optimal test for the calibration of predictive models](https://mlsanity.com/paper/2203.01850/) (2022)
- [The Price of Tolerance in Distribution Testing](https://mlsanity.com/paper/2106.13414/) (2021)
- [Minimax Optimal Regression over Sobolev Spaces via Laplacian Regularization on Neighborhood Graphs](https://mlsanity.com/paper/2106.01529/) (2021)
- [Selecting a number of voters for a voting ensemble](https://mlsanity.com/paper/2104.11833/) (2021)
- [Greedy equivalence search for nonparametric graphical models](https://mlsanity.com/paper/2406.17228/) (2024)
- [Instance-Optimal Uniformity Testing and Tracking](https://mlsanity.com/paper/2508.02637/) (2025)
- [The Minimax Risk in Testing Uniformity over Large Alphabets under Missing-Ball Alternatives](https://mlsanity.com/paper/2305.18111/) (2023)
- [Calibration Assessment for Nested Uncertainty Sets](https://mlsanity.com/paper/2610.04790/) (2026)

## Abstract (arXiv)

The statistical analysis of discrete data has been the subject of extensive statistical research dating back to the work of Pearson. In this survey we review some recently developed methods for testing hypotheses about high-dimensional multinomials. Traditional tests like the chi2 test and the likelihood ratio test can have poor power in the high-dimensional setting. Much of the research in this area has focused on finding tests with asymptotically Normal limits and developing (stringent) conditions under which tests have Normal limits. We argue that this perspective suffers from a significant deficiency: it can exclude many high-dimensional cases when - despite having non Normal null distributions - carefully designed tests can have high power. Finally, we illustrate that taking a minimax perspective and considering refinements of this perspective can lead naturally to powerful and practical tests.