A friendly proof of the Berry-Esseen theorem
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911425959559168 |
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| author | Vershynin, Roman |
| author_facet | Vershynin, Roman |
| contents | A gem of classical probability, the Berry-Esseen theorem provides a non-asymptotic form of the central limit theorem. This note gives a friendly and intuitive exposition of the classical Fourier-analytic proof of Esseen's smoothing inequality and, as a consequence, a general Berry-Esseen theorem for non-i.i.d random variables. The exposition is suitable for use in a basic graduate course in probability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06234 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A friendly proof of the Berry-Esseen theorem Vershynin, Roman Probability 60F05 (Primary), 60-02 (Secondary) A gem of classical probability, the Berry-Esseen theorem provides a non-asymptotic form of the central limit theorem. This note gives a friendly and intuitive exposition of the classical Fourier-analytic proof of Esseen's smoothing inequality and, as a consequence, a general Berry-Esseen theorem for non-i.i.d random variables. The exposition is suitable for use in a basic graduate course in probability. |
| title | A friendly proof of the Berry-Esseen theorem |
| topic | Probability 60F05 (Primary), 60-02 (Secondary) |
| url | https://arxiv.org/abs/2602.06234 |