论文标题
最佳的接近度测试（复杂）简单的离散分布
Optimal Closeness Testing of Discrete Distributions Made (Complex) Simple
论文作者
论文摘要
在本说明中，我们重新审视了Diakonikolas，Gouleakis，Kane，Peebles和Price（2021）的最新工作，并提供了其主要结果的替代证明。我们的论点不依赖于泊松随机变量的任何特定属性（例如稳定性和分裂性），也不依赖于任何“聪明的技巧”，而是基于将任何随机变量与其特征函数积分的绝对值期望相关的身份相关的身份： \ [ \ Mathbb { \] 我们的论点虽然没有技术方面，但在概念上可以说是更简单，更一般的。我们希望该技术可以在分发测试中找到其他应用。
In this note, we revisit the recent work of Diakonikolas, Gouleakis, Kane, Peebles, and Price (2021), and provide an alternative proof of their main result. Our argument does not rely on any specific property of Poisson random variables (such as stability and divisibility) nor on any "clever trick," but instead on an identity relating the expectation of the absolute value of any random variable to the integral of its characteristic function: \[ \mathbb{E}[|X|] = \frac{2}π\int_0^\infty \frac{1-\Re(\mathbb{E}[e^{i tX}])}{t^2}\, dt \] Our argument, while not devoid of technical aspects, is arguably conceptually simpler and more general; and we hope this technique can find additional applications in distribution testing.
