Concentration Inequalities for Statistical Inference
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866929722906116096 |
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| author | Zhang, Huiming Chen, Song Xi |
| author_facet | Zhang, Huiming Chen, Song Xi |
| contents | This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to sub-exponential, sub-Gamma, and sub-Weibull random variables, and from the mean to the maximum concentration. This review provides results in these settings with some fresh new results. Given the increasing popularity of high-dimensional data and inference, results in the context of high-dimensional linear and Poisson regressions are also provided. We aim to illustrate the concentration inequalities with known constants and to improve existing bounds with sharper constants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_02258 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Concentration Inequalities for Statistical Inference Zhang, Huiming Chen, Song Xi Statistics Theory Machine Learning Probability 60F10, 60G50, 62E17 This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to sub-exponential, sub-Gamma, and sub-Weibull random variables, and from the mean to the maximum concentration. This review provides results in these settings with some fresh new results. Given the increasing popularity of high-dimensional data and inference, results in the context of high-dimensional linear and Poisson regressions are also provided. We aim to illustrate the concentration inequalities with known constants and to improve existing bounds with sharper constants. |
| title | Concentration Inequalities for Statistical Inference |
| topic | Statistics Theory Machine Learning Probability 60F10, 60G50, 62E17 |
| url | https://arxiv.org/abs/2011.02258 |