Concentration inequalities for the sum in sampling without replacement: an approach via majorization
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916662931881984 |
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| author | Ai, Jianhang Kuželka, Ondřej Pelekis, Christos |
| author_facet | Ai, Jianhang Kuželka, Ondřej Pelekis, Christos |
| contents | Let $P=(x_1,\ldots,x_n)$ be a population consisting of $n\ge 2$ real numbers whose sum is zero, and let $k <n$ be a positive integer. We sample $k$ elements from $P$ without replacement and denote by $X_P$ the sum of the elements in our sample. In this article, using ideas from the theory of majorization, we deduce non-asymptotic lower and upper bounds on the probability that $X_P$ exceeds its expected value. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20473 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Concentration inequalities for the sum in sampling without replacement: an approach via majorization Ai, Jianhang Kuželka, Ondřej Pelekis, Christos Probability Statistics Theory Let $P=(x_1,\ldots,x_n)$ be a population consisting of $n\ge 2$ real numbers whose sum is zero, and let $k <n$ be a positive integer. We sample $k$ elements from $P$ without replacement and denote by $X_P$ the sum of the elements in our sample. In this article, using ideas from the theory of majorization, we deduce non-asymptotic lower and upper bounds on the probability that $X_P$ exceeds its expected value. |
| title | Concentration inequalities for the sum in sampling without replacement: an approach via majorization |
| topic | Probability Statistics Theory |
| url | https://arxiv.org/abs/2503.20473 |