## Electronic Journal of Probability

### Wasserstein-2 bounds in normal approximation under local dependence

Xiao Fang

#### 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.

#### Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1554775414

Digital Object Identifier
doi:10.1214/19-EJP301

Mathematical Reviews number (MathSciNet)
MR3940765

Zentralblatt MATH identifier
1412.60043

Subjects
Primary: 60F05: Central limit and other weak theorems

#### Citation

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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