Electronic Journal of Probability

Wasserstein-2 bounds in normal approximation under local dependence

Xiao Fang

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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.

Article information

Electron. J. Probab., Volume 24 (2019), paper no. 35, 14 pp.

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

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems

central limit theorem local dependence Erdős-Rényi random graph Stein’s method U-statistics Wasserstein-2 distance

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Fang, Xiao. Wasserstein-2 bounds in normal approximation under local dependence. Electron. J. Probab. 24 (2019), paper no. 35, 14 pp. doi:10.1214/19-EJP301. https://projecteuclid.org/euclid.ejp/1554775414

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