论文标题
独立随机变量功能的Berry-Esseen边界
Berry-Esseen bounds for functionals of independent random variables
论文作者
论文摘要
我们基于混乱的方法来得出独立随机变量的一般功能的浆果 - 近似界限。我们的结果适用于$ u $统计量，满足了在Hoffding意义上可分解性的弱假设，并产生了Kolmogorov距离界限，而不是先前在退化$ u $ statistics特殊情况下得出的Wasserstein界限。独立随机变量的任意序列的线性和二次功能作为特定情况，具有新的第四次界限，并应用于Hoffing分解，加权$ U $统计量，二次形式和随机子图的应用。在二次形式的情况下，我们的结果恢复并改善了文献中可用的界限，并适用于具有非空对角的矩阵。
We derive Berry-Esseen approximation bounds for general functionals of independent random variables, based on chaos expansions methods. Our results apply to $U$-statistics satisfying the weak assumption of decomposability in the Hoeffding sense, and yield Kolmogorov distance bounds instead of the Wasserstein bounds previously derived in the special case of degenerate $U$-statistics. Linear and quadratic functionals of arbitrary sequences of independent random variables are included as particular cases, with new fourth moment bounds, and applications are given to Hoeffding decompositions, weighted $U$-statistics, quadratic forms, and random subgraph weighing. In the case of quadratic forms, our results recover and improve the bounds available in the literature, and apply to matrices with non-empty diagonals.
