# Local minimax rates for closeness testing of discrete distributions

arXiv: https://arxiv.org/abs/1902.01219 · HTML: https://mlsanity.com/paper/1902.01219/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Feb 2019.

## Built on by (most cited first, 2 of 2)

- [Sparse Signal Detection in Heteroscedastic Gaussian Sequence Models: Sharp Minimax Rates](https://mlsanity.com/paper/2211.08580/) (2022)
- [Nonasymptotic one-and two-sample tests in high dimension with unknown covariance structure](https://mlsanity.com/paper/2109.01730/) (2021)

## Abstract (arXiv)

We consider the closeness testing problem for discrete distributions. The goal is to distinguish whether two samples are drawn from the same unspecified distribution, or whether their respective distributions are separated in L1-norm. In this paper, we focus on adapting the rate to the shape of the underlying distributions, i.e. we consider textita local minimax setting. We provide, to the best of our knowledge, the first local minimax rate for the separation distance up to logarithmic factors, together with a test that achieves it. In view of the rate, closeness testing turns out to be substantially harder than the related one-sample testing problem over a wide range of cases.