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arXiv · 2503.20473

Concentration inequalities for the sum in sampling without replacement: an approach via majorization

Jianhang Ai·Ondřej Kuželka·Christos Pelekis
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Abstract

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.

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Jianhang Ai, Ondřej Kuželka, Christos Pelekis. 2025-03-26. Concentration inequalities for the sum in sampling without replacement: an approach via majorization. https://arxiv.org/abs/2503.20473

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