AI 中文总结
该研究针对独立未必同分布的随机和，开发新型近似零偏变换推导$L^1$界，将其应用于含异常值抽样、汽车保险索赔及生成式AI响应时间等实际场景。
AI 中文摘要
我们针对随机和的检验函数与标准正态随机变量的差值推导了$L^1$界，其中假设求和项相互独立但未必同分布。该界通过专门为随机和开发的新型近似零偏变换版本得到。尽管放宽了同分布假设，此界的阶仍为$1/\sqrt{n}$，与文献中在求和项数量满足相同分布假设下的现有界阶一致。随后将主要结果应用于三个实际场景：含异常值简单随机抽样得到的随机和、总保险索赔额以及生成式AI的响应时间。
英文摘要
We develop $L^1$ bounds for the difference between a test function of a random sum and a standard normal random variable, where the summands are assumed to be independent but not necessarily identically distributed. The bounds are obtained through a new version of the approximate zero bias transformation specifically developed for random sums. Although the identical distribution assumption is relaxed, the bounds are of order $1/\sqrt{n}$, matching the order of existing bounds in the literature under the same distributional assumption on the number of summands. The main results are then applied to three real-world settings: random sums obtained from simple random sampling with outliers, total insurance claims, and generative AI response times.
Comments25 pages
