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\Hos--Rényi random graphs.
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