Normal approximation for generalized U-statistics and weighted random graphs

Abstract

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.