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2019 Wasserstein-2 bounds in normal approximation under local dependence
Xiao Fang
Electron. J. Probab. 24: 1-14 (2019). DOI: 10.1214/19-EJP301

Abstract

We obtain a general bound for the Wasserstein-2 distance in normal approximation for sums of locally dependent random variables. The proof is based on an asymptotic expansion for expectations of second-order differentiable functions of the sum. We apply the main result to obtain Wasserstein-2 bounds in normal approximation for sums of $m$-dependent random variables, U-statistics and subgraph counts in the Erdős-Rényi random graph. We state a conjecture on Wasserstein-$p$ bounds for any positive integer $p$ and provide supporting arguments for the conjecture.

Citation

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Xiao Fang. "Wasserstein-2 bounds in normal approximation under local dependence." Electron. J. Probab. 24 1 - 14, 2019. https://doi.org/10.1214/19-EJP301

Information

Received: 1 February 2019; Accepted: 24 March 2019; Published: 2019
First available in Project Euclid: 9 April 2019

zbMATH: 1412.60043
MathSciNet: MR3940765
Digital Object Identifier: 10.1214/19-EJP301

Subjects:
Primary: 60F05

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