On existence and uniqueness of univariate Stein kernels
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913695153520640 |
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| author | Döbler, Christian |
| author_facet | Döbler, Christian |
| contents | We completely characterize the class of univariate distributions allowing for a Stein kernel and illustrate our result by means of some concrete distributions. Moreover, we apply our findings to prove a quantitative version of the central limit theorem with optimal rate $n^{-1/2}$ in total variation distance for i.i.d. random variables whose distribution belongs to that class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03910 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On existence and uniqueness of univariate Stein kernels Döbler, Christian Probability 60E05, 60F05 We completely characterize the class of univariate distributions allowing for a Stein kernel and illustrate our result by means of some concrete distributions. Moreover, we apply our findings to prove a quantitative version of the central limit theorem with optimal rate $n^{-1/2}$ in total variation distance for i.i.d. random variables whose distribution belongs to that class. |
| title | On existence and uniqueness of univariate Stein kernels |
| topic | Probability 60E05, 60F05 |
| url | https://arxiv.org/abs/2502.03910 |