Normal approximation for sums of discrete $U$-statistics - application to Kolmogorov bounds in random subgraph counting
Probability
2018-06-15 v1
Abstract
We derive normal approximation bounds in the Kolmogorov distance for sums of discrete multiple integrals and -statistics made of independent Bernoulli random variables. Such bounds are applied to normal approximation for the renormalized subgraphs counts in the Erd{\H o}s-R\'enyi random graph. This approach completely solves a long-standing conjecture in the general setting of arbitrary graph counting, while recovering and improving recent results derived for triangles as well as results using the Wasserstein distance.
Keywords
Cite
@article{arxiv.1806.05339,
title = {Normal approximation for sums of discrete $U$-statistics - application to Kolmogorov bounds in random subgraph counting},
author = {Nicolas Privault and Grzegorz Serafin},
journal= {arXiv preprint arXiv:1806.05339},
year = {2018}
}