Concentration inequalities using approximate zero bias couplings with applications to Hoeffding’s statistic under the Ewens distribution

Nathakhun Wiroonsri

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 19, 6734-6750

Abstract: We prove concentration inequalities of the form P(Y≥t)≤ exp (−B(t)) for a random variable Y with mean zero and variance σ2 using a coupling technique from Stein’s method that is so-called approximate zero bias couplings. Applications to the Hoeffding’s statistic where the random permutation has the Ewens distribution with parameter θ>0 are also presented. A few simulation experiments are then provided to visualize the tail probability of the Hoeffding’s statistic and our bounds. Based on the simulation results, our bounds work well especially when θ≤1.

Date: 2023
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DOI: 10.1080/03610926.2022.2032753

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