Sharper Concentration Inequalities for Median-of-Mean Processes-Reference-Cited by-同舟云学术

Sharper Concentration Inequalities for Median-of-Mean Processes

Published:2023-08-30 Issue:17 Volume:11 Page:3730
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Teng Guangqiang¹,Li Yanpeng²^ORCID,Tian Boping¹^ORCID,Li Jie³

Affiliation:

1. School of Mathematics, Harbin Institute of Technology, Harbin 150001, China

2. Department of Statistics and Data Science, National University of Singapore, 21 Lowr Kent Ridge Road, Singapore 119077, Singapore

3. 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.

Funder

China Postdoctoral Science Foundation

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/17/3730/pdf

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