mlsanityData to 13 Oct 2026

Randomized and Exchangeable Improvements of Markov's, Chebyshev's and Chernoff's Inequalities

arXiv 2304.02611 ↗First posted 5 Apr 2023math.ST cs.IT math.ITcited by 15

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Abstract (arXiv)

We present simple randomized and exchangeable improvements of Markov's inequality, as well as Chebyshev's inequality and Chernoff bounds. Our variants are never worse and typically strictly more powerful than the original inequalities. The proofs are short and elementary, and can easily yield similarly randomized or exchangeable versions of a host of other inequalities that employ Markov's inequality as an intermediate step. We point out some simple statistical applications involving tests that combine dependent e-values. In particular, we uniformly improve the power of universal inference, and obtain tighter betting-based nonparametric confidence intervals. Simulations reveal nontrivial gains in power (and no losses) in a variety of settings.

Key facts. Cited by 15 papers in the map (data through 13 Oct 2026). First posted on arXiv 5 Apr 2023.

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2023: 1; 2024: 6; 2025: 6; 2026: 2.

15 papers.

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  1. 2025Reliable Text-to-SQL with Adaptive Abstentioncited by 20
  2. 2025E-valuator: Reliable Agent Verifiers with Sequential Hypothesis Testingcited by 16
  3. 2024Conformal online model aggregationcited by 11
  4. 2024Online Detection of LLM-Generated Texts via Sequential Hypothesis Testing by Bettingcited by 11
  5. 2025Improving the statistical efficiency of cross-conformal predictioncited by 5
  6. 2025Optimistic Interior Point Methods for Sequential Hypothesis Testing by Bettingcited by 4
  7. 2024Combining Evidence Across Filtrationscited by 3
  8. 2023Anytime-valid t-tests and confidence sequences for Gaussian means with unknown variancecited by 2
  9. 2024Sharp Matrix Empirical Bernstein Inequalitiescited by 2
  10. 2025Derandomizing Simultaneous Confidence Regions for Band-Limited Functions by Improved Norm Bounds and Majority-Voting Schemescited by 1
  11. 2026Concentration Inequalities for Exchangeable Tensors and Matrix-valued Datacited by 1
  12. 2024Positive Semidefinite Matrix Supermartingalescited by 0
3 more
  1. 2024Data-light Uncertainty Set Merging with Admissibilitycited by 0
  2. 2025On the Precise Asymptotics of Universal Inferencecited by 0
  3. 2026Set-Preserving Calibration from Conformal P-Values to E-Valuescited by 0