Sharp One-Dimensional Sub-Gaussian Comparison in Convex Order
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911633145593856 |
|---|---|
| author | Zhang, Yihan |
| author_facet | Zhang, Yihan |
| contents | We prove that any random variable $X$ whose moment generating function is point-wise upper bounded by that of $ G \sim \mathcal{N}(0,1) $ must be dominated by $ G/\mathbb{E}[|G|] $ in convex order, meaning $ \mathbb{E}[f(X)] \le \mathbb{E}[f(G/\mathbb{E}[|G|])] $ for all convex $f$. Equality is attained by taking $ X \sim \mathrm{Unif}(\{-1,1\}) $ and $ f(x) = |x| $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26819 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp One-Dimensional Sub-Gaussian Comparison in Convex Order Zhang, Yihan Probability Information Theory Statistics Theory Machine Learning We prove that any random variable $X$ whose moment generating function is point-wise upper bounded by that of $ G \sim \mathcal{N}(0,1) $ must be dominated by $ G/\mathbb{E}[|G|] $ in convex order, meaning $ \mathbb{E}[f(X)] \le \mathbb{E}[f(G/\mathbb{E}[|G|])] $ for all convex $f$. Equality is attained by taking $ X \sim \mathrm{Unif}(\{-1,1\}) $ and $ f(x) = |x| $. |
| title | Sharp One-Dimensional Sub-Gaussian Comparison in Convex Order |
| topic | Probability Information Theory Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2604.26819 |