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Worst-case Chernoff bounds for sums of random variables with known means and unequal ranges

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  • Loper, Jackson
  • Regier, Jeffrey

Abstract

We construct a new tail bound for the sum of independent random variables for situations in which the expected value of the sum is known and each random variable lies within a specified interval, which may be different for each variable. This new bound can be computed by solving a two-dimensional convex optimization problem. Simulations demonstrate that the new bound is often substantially tighter than Hoeffding’s inequality for cases in which both bounds are applicable.

Suggested Citation

  • Loper, Jackson & Regier, Jeffrey, 2026. "Worst-case Chernoff bounds for sums of random variables with known means and unequal ranges," Statistics & Probability Letters, Elsevier, vol. 235(C).
    • Handle: RePEc:eee:stapro:v:235:y:2026:i:c:s0167715226001069
    DOI: 10.1016/j.spl.2026.110742
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