Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.11489 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914469236441088 |
|---|---|
| author | Yu, Zhen Hong Miao, Yu |
| author_facet | Yu, Zhen Hong Miao, Yu |
| contents | In the present paper, we derive Berry-Esseen bounds for the estimation of diversity indices on countable alphabets. A general non-asymptotic convergence rate is established for the plug-in estimator of a wide class of indices, including Simpson's index and Reńyi's entropy. For the practically crucial case of Shannon entropy, we provide explicit Berry-Esseen bounds for the standard plug-in estimator, as well as for two widely used bias-corrected variants, the Miller-Madow and the jackknife estimators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11489 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Berry-Esseen bounds for estimators of entropy and diversity indices on countable alphabets Yu, Zhen Hong Miao, Yu Probability In the present paper, we derive Berry-Esseen bounds for the estimation of diversity indices on countable alphabets. A general non-asymptotic convergence rate is established for the plug-in estimator of a wide class of indices, including Simpson's index and Reńyi's entropy. For the practically crucial case of Shannon entropy, we provide explicit Berry-Esseen bounds for the standard plug-in estimator, as well as for two widely used bias-corrected variants, the Miller-Madow and the jackknife estimators. |
| title | Berry-Esseen bounds for estimators of entropy and diversity indices on countable alphabets |
| topic | Probability |
| url | https://arxiv.org/abs/2604.11489 |