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Sharper Concentration Inequalities for Median-of-Mean Processes

Author

Listed:
  • Guangqiang Teng

    (School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
    These authors contributed equally to this work.)

  • Yanpeng Li

    (Department of Statistics and Data Science, National University of Singapore, 21 Lowr Kent Ridge Road, Singapore 119077, Singapore
    These authors contributed equally to this work.)

  • Boping Tian

    (School of Mathematics, Harbin Institute of Technology, Harbin 150001, China)

  • Jie Li

    (School of Statistics, Renmin University of China, Beijing 100872, China)

Abstract

The Median-of-Mean (MoM) estimation is an efficient statistical method for handling data with contamination. In this paper, we propose a variance-dependent MoM estimation method using the tail probability of a binomial distribution. The bound of this method is better than the classical Hoeffding method under mild conditions. This method is then used to study the concentration of variance-dependent MoM empirical processes and sub-Gaussian intrinsic moment norm. Finally, we give the bound of the variance-dependent MoM estimator with distribution-free contaminated data.

Suggested Citation

  • Guangqiang Teng & Yanpeng Li & Boping Tian & Jie Li, 2023. "Sharper Concentration Inequalities for Median-of-Mean Processes," Mathematics, MDPI, vol. 11(17), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3730-:d:1228973
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