可交换随机变量加权和的更紧Hoeffding界
A Sharper Hoeffding Bound for Weighted Sums of Exchangeable Random Variables
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中文总结 AI 辅助
本文针对有界可交换随机变量加权和，证明了更紧的Hoeffding型矩生成函数界，改进了现有膨胀因子的阶并给出显式常数，还证明了逆总体大小膨胀的不可避免性。
中文摘要 AI 辅助
我们针对以有限总体均值为中心的有界可交换随机变量加权和，证明了一类Hoeffding型矩生成函数界。该界将近期加权可交换Hoeffding不等式中的有限总体膨胀因子，从对数阶改进为最优的逆总体大小阶，并给出了显式常数。证明将问题约化为汉明切片，确定了相关对称变分问题的两级极值器，应用了超几何鞅界。我们还给出了一个下界，表明逆总体大小的膨胀是不可避免的。
英文摘要
We prove a Hoeffding-type moment generating function bound for weighted sums of bounded exchangeable random variables centered by their finite-population average. The bound reduces the excess inflation above one in a recent weighted exchangeable Hoeffding inequality from order $(\log N)/N$ to the rate-optimal order $1/N$, with an explicit constant. The proof reduces the problem to Hamming slices, identifies two-level extremizers for the relevant symmetric variational problem, and applies a hypergeometric martingale bound. We also give a lower bound showing that an excess inflation of order $1/N$ is unavoidable.
发表机构
- KAIST（韩国科学技术院）
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