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| Format: | Preprint |
| Publié: |
2022
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2206.00199 |
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| _version_ | 1866915691752325120 |
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| author | Wiroonsri, Nathakhun |
| author_facet | Wiroonsri, Nathakhun |
| 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 $θ\le 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_00199 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Concentration inequalities using approximate zero bias couplings with applications to Hoeffding's statistic under the Ewens distribution Wiroonsri, Nathakhun Probability 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 $θ\le 1$. |
| title | Concentration inequalities using approximate zero bias couplings with applications to Hoeffding's statistic under the Ewens distribution |
| topic | Probability |
| url | https://arxiv.org/abs/2206.00199 |