The Efron-Stein inequality for identically distributed pairs
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866911654655033344 |
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| author | Baslingker, Jnaneshwar Virág, Bálint |
| author_facet | Baslingker, Jnaneshwar Virág, Bálint |
| contents | We prove that the classical Efron--Stein inequality holds for independent exchangeable pairs \((X_i,Y_i)\). The same inequality fails for independent identically distributed pairs; a simple trigonometric counterexample shows that the trivial Cauchy--Schwarz bound of factor \(n\) is sharp. When each random variable takes at most \(k_i\) values, a useful bound still holds with explicit constant \(ρ(k)\le\max_i k_i/2\). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05388 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Efron-Stein inequality for identically distributed pairs Baslingker, Jnaneshwar Virág, Bálint Probability We prove that the classical Efron--Stein inequality holds for independent exchangeable pairs \((X_i,Y_i)\). The same inequality fails for independent identically distributed pairs; a simple trigonometric counterexample shows that the trivial Cauchy--Schwarz bound of factor \(n\) is sharp. When each random variable takes at most \(k_i\) values, a useful bound still holds with explicit constant \(ρ(k)\le\max_i k_i/2\). |
| title | The Efron-Stein inequality for identically distributed pairs |
| topic | Probability |
| url | https://arxiv.org/abs/2605.05388 |