Efficient computation of tight approximations to Chernoff bounds

Daniel Shiu ()
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Daniel Shiu: Arqit Quantum Inc.

Computational Statistics, 2023, vol. 38, issue 1, No 7, 133-147

Abstract: Abstract Chernoff bounds are a powerful application of the Markov inequality to produce strong bounds on the tails of probability distributions. They are often used to bound the tail probabilities of sums of Poisson trials, or in regression to produce conservative confidence intervals for the parameters of such trials. The bounds provide expressions for the tail probabilities that can be inverted for a given probability/confidence to provide tail intervals. The inversions involve the solution of transcendental equations and it is often convenient to substitute approximations that can be exactly solved e.g. by the quadratic equation. In this paper we introduce approximations for the Chernoff bounds whose inversion can be exactly solved with a quadratic equation, but which are closer approximations than those adopted previously.

Keywords: Chernoff bounds; Tail distributions; Concentration inequalities; Poisson trials (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:compst:v:38:y:2023:i:1:d:10.1007_s00180-022-01219-2

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DOI: 10.1007/s00180-022-01219-2

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