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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2206.00199 |
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Table of Contents:
- We prove concentration inequalities of the form $P(Y \ge t) \le \exp(-B(t))$ for a random variable $Y$ with mean zero and variance $σ^2$ 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 $θ\le 1$.