Concentration inequalities via zero bias couplings

Larry Goldstein and Ümit Işlak

Statistics & Probability Letters, 2014, vol. 86, issue C, 17-23

Abstract: The tails of the distribution of a mean zero, variance σ2 random variable Y satisfy concentration of measure inequalities of the form P(Y≥t)≤exp(−B(t)) forB(t)=t22(σ2+ct)for t≥0,andB(t)=tc(logt−loglogt−σ2c)for t>e whenever there exists a zero biased coupling of Y bounded by c, under suitable conditions on the existence of the moment generating function of Y. These inequalities apply in cases where Y is not a function of independent variables, such as for the Hoeffding statistic Y=∑i=1naiπ(i) where A=(aij)1≤i,j≤n∈Rn×n and the permutation π has the uniform distribution over the symmetric group, and when its distribution is constant on cycle type.

Keywords: Tail probabilities; Zero bias coupling; Stein’s method (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2013.12.001

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