Sharper Concentration Inequalities for Median-of-Mean Processes

Guangqiang Teng, Yanpeng Li, Boping Tian () and Jie Li ()
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Guangqiang Teng: School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Yanpeng Li: Department of Statistics and Data Science, National University of Singapore, 21 Lowr Kent Ridge Road, Singapore 119077, Singapore
Boping Tian: School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Jie Li: School of Statistics, Renmin University of China, Beijing 100872, China

Mathematics, 2023, vol. 11, issue 17, 1-12

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.

Keywords: concentration inequality; Median-of-Mean; robust machine learning; contaminated data (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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