Optimal distribution-free concentration for the log-likelihood function of Bernoulli variables
Abstract This paper aims to establish distribution-free concentration inequalities for the log-likelihood function of Bernoulli variables, which means that the tail bounds are independent of the parameters. Moreover, Bernstein’s and Bennett’s inequalities with optimal constants are obtained. The sim...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-06-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-023-02995-1 |
| _version_ | 1797806438091849728 |
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| author | Zhonggui Ren |
| author_facet | Zhonggui Ren |
| author_sort | Zhonggui Ren |
| collection | DOAJ |
| description | Abstract This paper aims to establish distribution-free concentration inequalities for the log-likelihood function of Bernoulli variables, which means that the tail bounds are independent of the parameters. Moreover, Bernstein’s and Bennett’s inequalities with optimal constants are obtained. The simulation study shows significant improvements over the previous results. |
| first_indexed | 2024-03-13T06:07:19Z |
| format | Article |
| id | doaj.art-6d090b7c7842436298ffdb86016a8dd2 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-03-13T06:07:19Z |
| publishDate | 2023-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-6d090b7c7842436298ffdb86016a8dd22023-06-11T11:28:14ZengSpringerOpenJournal of Inequalities and Applications1029-242X2023-06-012023111110.1186/s13660-023-02995-1Optimal distribution-free concentration for the log-likelihood function of Bernoulli variablesZhonggui Ren0College of Foundation Science, Harbin University of CommerceAbstract This paper aims to establish distribution-free concentration inequalities for the log-likelihood function of Bernoulli variables, which means that the tail bounds are independent of the parameters. Moreover, Bernstein’s and Bennett’s inequalities with optimal constants are obtained. The simulation study shows significant improvements over the previous results.https://doi.org/10.1186/s13660-023-02995-1Bernstein’s inequalityBennett’s inequalityLog-likelihood functionBernoulli distribution |
| spellingShingle | Zhonggui Ren Optimal distribution-free concentration for the log-likelihood function of Bernoulli variables Journal of Inequalities and Applications Bernstein’s inequality Bennett’s inequality Log-likelihood function Bernoulli distribution |
| title | Optimal distribution-free concentration for the log-likelihood function of Bernoulli variables |
| title_full | Optimal distribution-free concentration for the log-likelihood function of Bernoulli variables |
| title_fullStr | Optimal distribution-free concentration for the log-likelihood function of Bernoulli variables |
| title_full_unstemmed | Optimal distribution-free concentration for the log-likelihood function of Bernoulli variables |
| title_short | Optimal distribution-free concentration for the log-likelihood function of Bernoulli variables |
| title_sort | optimal distribution free concentration for the log likelihood function of bernoulli variables |
| topic | Bernstein’s inequality Bennett’s inequality Log-likelihood function Bernoulli distribution |
| url | https://doi.org/10.1186/s13660-023-02995-1 |
| work_keys_str_mv | AT zhongguiren optimaldistributionfreeconcentrationfortheloglikelihoodfunctionofbernoullivariables |