Sharper Concentration Inequalities for Median-of-Mean Processes
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 met...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/17/3730 |
| _version_ | 1797582180293017600 |
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| author | Guangqiang Teng Yanpeng Li Boping Tian Jie Li |
| author_facet | Guangqiang Teng Yanpeng Li Boping Tian Jie Li |
| author_sort | Guangqiang Teng |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T23:17:14Z |
| format | Article |
| id | doaj.art-450d931d96134b2cab03a8c1257b4ff3 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T23:17:14Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-450d931d96134b2cab03a8c1257b4ff32023-11-19T08:31:21ZengMDPI AGMathematics2227-73902023-08-011117373010.3390/math11173730Sharper Concentration Inequalities for Median-of-Mean ProcessesGuangqiang Teng0Yanpeng Li1Boping Tian2Jie Li3School of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Statistics and Data Science, National University of Singapore, 21 Lowr Kent Ridge Road, Singapore 119077, SingaporeSchool of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaSchool of Statistics, Renmin University of China, Beijing 100872, ChinaThe 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.https://www.mdpi.com/2227-7390/11/17/3730concentration inequalityMedian-of-Meanrobust machine learningcontaminated data |
| spellingShingle | Guangqiang Teng Yanpeng Li Boping Tian Jie Li Sharper Concentration Inequalities for Median-of-Mean Processes Mathematics concentration inequality Median-of-Mean robust machine learning contaminated data |
| title | Sharper Concentration Inequalities for Median-of-Mean Processes |
| title_full | Sharper Concentration Inequalities for Median-of-Mean Processes |
| title_fullStr | Sharper Concentration Inequalities for Median-of-Mean Processes |
| title_full_unstemmed | Sharper Concentration Inequalities for Median-of-Mean Processes |
| title_short | Sharper Concentration Inequalities for Median-of-Mean Processes |
| title_sort | sharper concentration inequalities for median of mean processes |
| topic | concentration inequality Median-of-Mean robust machine learning contaminated data |
| url | https://www.mdpi.com/2227-7390/11/17/3730 |
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