改进了离散分布在ℓ∞范数下的估计精度，解决多个开放问题。
Improved Distribution Estimation in $\ell_\infty$
- 提出期望与高概率下的最优风险界
- 实现比前人更紧的误差上界，且可完全基于数据计算
- 适用于对分布估计精度要求高的统计学习场景
本文针对离散概率分布的ℓ∞范数估计问题，给出了改进的极小极大界，包括期望意义上的最优界和高概率尾部界。解决了Kontorovich与Painsky（JMLR, 2025）提出的若干开放问题，包括实现他们提出的最紧风险界的完全经验版本，并确定了最坏情况下的极端分布形式。同时报告了具有启发性的实验结果。
原文摘要 · Abstract (English)
We present improved bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These include minimax bounds in expectation and high-probability tail bounds. We resolve some of the open questions posed in Kontorovich and Painsky (JMLR, 2025) -- including a fully empirical version of the tightest risk bound they presented and identifying the form of the worst-case extremal distribution. Encouraging empirical results are reported as well.
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