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Decoupling and randomization for double-indexed permutation statistics

Author

Listed:
  • Mingxuan Zou
  • Jingfan Xu
  • Peng Ding
  • Fang Han

Abstract

This paper introduces a version of decoupling and randomization to establish concentration inequalities for double-indexed permutation statistics. The results yield, among other applications, a new combinatorial Hanson-Wright inequality and a new combinatorial Bennett inequality. Several illustrative examples from rank-based statistics, graph-based statistics, and causal inference are also provided.

Suggested Citation

  • Mingxuan Zou & Jingfan Xu & Peng Ding & Fang Han, 2026. "Decoupling and randomization for double-indexed permutation statistics," Papers 2601.20018, arXiv.org, revised Mar 2026.
    • Handle: RePEc:arx:papers:2601.20018
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    References listed on IDEAS

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    1. Holger Sambale & Arthur Sinulis, 2022. "Concentration Inequalities on the Multislice and for Sampling Without Replacement," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2712-2737, December.
    2. Fang Han, 2024. "An Introduction to Permutation Processes (version 0.5)," Papers 2407.09664, arXiv.org.
    3. Holger Dette & Karl F. Siburg & Pavel A. Stoimenov, 2013. "A Copula-Based Non-parametric Measure of Regression Dependence," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(1), pages 21-41, March.
    4. Lihua Lei & Peng Ding, 2021. "Regression adjustment in completely randomized experiments with a diverging number of covariates [Covariance adjustments for the analysis of randomized field experiments]," Biometrika, Biometrika Trust, vol. 108(4), pages 815-828.
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