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PreprintCC BY 4.0arXiv

A Sharper Hoeffding Bound for Weighted Sums of Exchangeable Random Variables

  • Seongchan Lee
  • Ilmun Kim
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Abstract

We prove a Hoeffding-type moment generating function bound for weighted sums of bounded exchangeable random variables centered by their finite-population average. The bound reduces the excess inflation above one in a recent weighted exchangeable Hoeffding inequality from order (log N)/N to the rate-optimal order 1/N, with an explicit constant. The proof reduces the problem to Hamming slices, identifies two-level extremizers for the relevant symmetric variational problem, and applies a hypergeometric martingale bound. We also give a lower bound showing that an excess inflation of order 1/N is unavoidable.

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Cite

BibTeXRIS
BibTeX
@misc{lee2026sharper,
  title = {{A Sharper Hoeffding Bound for Weighted Sums of Exchangeable Random Variables}},
  author = {Seongchan Lee and Ilmun Kim},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.04900},
  eprint = {2608.04900},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.04900},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Sharper Hoeffding Bound for Weighted Sums of Exchangeable Random Variables
AU  - Seongchan Lee
AU  - Ilmun Kim
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.04900
UR  - https://arxiv.org/abs/2608.04900
AB  - We prove a Hoeffding-type moment generating function bound for weighted sums of bounded exchangeable random variables centered by their finite-population average. The bound reduces the excess inflation above one in a recent weighted exchangeable Hoeffding inequality from order (log N)/N to the rate-optimal order 1/N, with an explicit constant. The proof reduces the problem to Hamming slices, identifies two-level extremizers for the relevant symmetric variational problem, and applies a hypergeometric martingale bound. We also give a lower bound showing that an excess inflation of order 1/N is unavoidable.
ER  -