%0 Journal Article %1 barbour2018central %A Barbour, A. D. %A Ross, Nathan %A Wen, Yuting %D 2018 %K stein %T Central moment inequalities using Stein's method %U http://arxiv.org/abs/1802.10225 %X 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 positive or 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 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 Erd\Hos--Rényi random graphs.

@article{barbour2018central, abstract = {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 positive or 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 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 Erd\H{o}s--R\'enyi random graphs.}, added-at = {2018-03-02T16:36:43.000+0100}, author = {Barbour, A. D. and Ross, Nathan and Wen, Yuting}, biburl = {https://www.bibsonomy.org/bibtex/2686b91a3d5d791c1806347e46a2f3817/claired}, description = {Central moment inequalities using Stein's method}, interhash = {7979d7ab71298e9007598828a839dbf5}, intrahash = {686b91a3d5d791c1806347e46a2f3817}, keywords = {stein}, note = {cite arxiv:1802.10225Comment: 21 pages}, timestamp = {2018-03-02T16:36:43.000+0100}, title = {Central moment inequalities using Stein's method}, url = {http://arxiv.org/abs/1802.10225}, year = 2018 }