Concentration inequalities quantify random fluctuations of functions of random variables, typically by bounding the probability that such a function differs from its expected value by more than a certain amount. In this paper, we extend Hoeffding’s inequality and Bernstein’s inequality for U-statistics to the setting of sampling without replacement from a finite population.

中文翻译：

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无需替换的 U 统计量的 Hoeffding 和 Bernstein 不等式

浓度不等式量化随机变量函数的随机波动，通常通过限制此类函数与其预期值的差异超过一定量的概率。在本文中，我们将 U 统计量的 Hoeffding 不等式和 Bernstein 不等式扩展到从有限总体中进行无替换抽样的设置。