Exponential Concentration Inequalities For Independent Random Vectors Under Sublinear Expectations
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915815604879360 |
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| author | Seyoum, Nahom |
| author_facet | Seyoum, Nahom |
| contents | Li and Hu recently established variance-type O(1/n) bounds for the sample mean of independent random vectors under sublinear expectations. We extend their results to the exponential concentration regime. For bounded, independent R^d-valued random vectors under a regular sublinear expectation, we prove: (i) a general concentration principle that reduces vector-valued tail bounds to scalar martingale inequalities via a three-layer architecture; (ii) an Azuma-Hoeffding inequality showing that the distance from the sample mean to the Minkowski average of the expectation sets has sub-Gaussian tails; (iii) a Bernstein inequality incorporating the variance parameter of Li and Hu, interpolating between sub-Gaussian and sub-exponential regimes; (iv) a dimension-free bound replacing the exponential covering prefactor with a polynomial one via the matrix Freedman inequality; and (v) an explicit construction demonstrating that the sub-Gaussian rate is optimal. To the best of our knowledge, these constitute the first exponential concentration inequalities for the multivariate sample mean under sublinear expectations in terms of the set-valued distance to the Minkowski average. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21465 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exponential Concentration Inequalities For Independent Random Vectors Under Sublinear Expectations Seyoum, Nahom Statistics Theory Probability Li and Hu recently established variance-type O(1/n) bounds for the sample mean of independent random vectors under sublinear expectations. We extend their results to the exponential concentration regime. For bounded, independent R^d-valued random vectors under a regular sublinear expectation, we prove: (i) a general concentration principle that reduces vector-valued tail bounds to scalar martingale inequalities via a three-layer architecture; (ii) an Azuma-Hoeffding inequality showing that the distance from the sample mean to the Minkowski average of the expectation sets has sub-Gaussian tails; (iii) a Bernstein inequality incorporating the variance parameter of Li and Hu, interpolating between sub-Gaussian and sub-exponential regimes; (iv) a dimension-free bound replacing the exponential covering prefactor with a polynomial one via the matrix Freedman inequality; and (v) an explicit construction demonstrating that the sub-Gaussian rate is optimal. To the best of our knowledge, these constitute the first exponential concentration inequalities for the multivariate sample mean under sublinear expectations in terms of the set-valued distance to the Minkowski average. |
| title | Exponential Concentration Inequalities For Independent Random Vectors Under Sublinear Expectations |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2602.21465 |