Open Access
2020 Central moment inequalities using Stein’s method
A.D. Barbour, Nathan Ross, Yuting Wen
Electron. J. Probab. 25: 1-21 (2020). DOI: 10.1214/20-EJP493


We derive explicit central moment inequalities for random variables that admit a Stein coupling, such as exchangeable pairs, size–bias couplings or local dependence, among others. The bounds are in terms of moments (not necessarily central) of variables in the Stein coupling, which are typically local in some sense, and therefore easier to bound. In cases where the Stein couplings have the kind of behaviour leading to good normal approximation, the central moments are closely bounded by those of a normal. We show how the bounds can be used to produce concentration inequalities, and compare them to those existing in related settings. Finally, we illustrate the power of the theory by bounding the central moments of sums of neighbourhood statistics in sparse Erdős–Rényi random graphs.


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A.D. Barbour. Nathan Ross. Yuting Wen. "Central moment inequalities using Stein’s method." Electron. J. Probab. 25 1 - 21, 2020.


Received: 18 February 2019; Accepted: 4 July 2020; Published: 2020
First available in Project Euclid: 7 August 2020

zbMATH: 07252723
MathSciNet: MR4136471
Digital Object Identifier: 10.1214/20-EJP493

Primary: 60C05 , 60E15

Keywords: Concentration inequalities , Erdős–Rényi random graph , Moment inequalities , Stein’s method

Vol.25 • 2020
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