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

Fuente: arXiv
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Main Authors: Ai, Jianhang, Kuželka, Ondřej, Pelekis, Christos
Format: Preprint
Published: 2025
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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