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February 2020 Normal approximation for sums of weighted $U$-statistics – application to Kolmogorov bounds in random subgraph counting
Nicolas Privault, Grzegorz Serafin
Bernoulli 26(1): 587-615 (February 2020). DOI: 10.3150/19-BEJ1141

Abstract

We derive normal approximation bounds in the Kolmogorov distance for sums of discrete multiple integrals and weighted $U$-statistics made of independent Bernoulli random variables. Such bounds are applied to normal approximation for the renormalized subgraph counts in the Erdős–Rényi random graph. This approach completely solves a long-standing conjecture in the general setting of arbitrary graph counting, while recovering recent results obtained for triangles and improving other bounds in the Wasserstein distance.

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Nicolas Privault. Grzegorz Serafin. "Normal approximation for sums of weighted $U$-statistics – application to Kolmogorov bounds in random subgraph counting." Bernoulli 26 (1) 587 - 615, February 2020. https://doi.org/10.3150/19-BEJ1141

Information

Received: 1 October 2018; Revised: 1 June 2019; Published: February 2020
First available in Project Euclid: 26 November 2019

MathSciNet: MR4036045
zbMATH: 07140510
Digital Object Identifier: 10.3150/19-BEJ1141

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

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Vol.26 • No. 1 • February 2020
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