We derive normal approximation bounds in the Wasserstein distance for sums of weighted U-statistics, based on a general distance bound for functionals of independent random variables of arbitrary distributions. Those bounds are applied to normal approximation for the combined weights of subgraphs in the Erdős-Rényi random graph, extending the graph counting results of [1] to the setting of graph weighting. Our approach relies on a general stochastic analytic framework for functionals of independent random sequences.
The Asymptotic Distribution of Randomly Weighted Sums and Self-normalized Sums
我们考虑自归一化和$T_{n}=\sum_{i=1}^{n}X_{i}Y_{i}/\sum_{i=1}^{n}Y_{i}$，其中${Y_{i} : i\geq 1}$是非负i.i.d.随机变量，并且${X_{i} : i\geq 1} $是i.i.d.随机变量，独立于${Y_{i} : i \geq 1}$。本文的主要结果是：T_PDMATHABMQ $ with finite expectation, if and only if $ Y_1$的每个连续极限律都是中心Feller类.
Robust Scale Estimation in Additive Noise via Weighted Order Statistics
Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México（墨西哥国立自治大学应用数学与系统研究所）；Centro de Investigación en Matemáticas, A.C.（墨西哥数学研究中心）
