We derive normal approximation bounds in the Wasserstein distance for sums of generalized 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 Barbour et al. (A central limit theorem for decomposable random variables with applications to random graphs, J. Combin. Theory Ser. B 47(2) (1989), pp. 125–145) to the setting of weighted graphs. Our approach relies on a general stochastic analytic framework for functionals of independent random sequences.

我们基于任意分布的独立随机变量的泛函的一般距离界限，推导出广义U统计量总和的 Wasserstein 距离中的正态近似界限。这些界限应用于 Erdős-Rényi 随机图中子图组合权重的正态近似，扩展了 Barbour等人的图计数结果。（A central limit theorem for decomposable random variables with applications to random graphs , J. Combin. Theory Ser. B 47(2) (1989), pp. 125–145）设置加权图。我们的方法依赖于独立随机序列泛函的一般随机分析框架。