Concentration inequalities using approximate zero bias couplings with applications to Hoeffding's statistic under the Ewens distribution
| Autor: | Wiroonsri, Nathakhun |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1080/03610926.2022.2032753 |
| Popis: | 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 $\sigma^2$ 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 $\theta>0$ 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 $\theta \le 1$. Comment: This preprint has not undergone peer review (when applicable) or any post-submission improvements or corrections. The Version of Record of this article is published in Communications in Statistics - Theory and Methods (2022), and is available online at https://doi.org/10.1080/03610926.2022.2032753 |
| Databáze: | arXiv |
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