Concentration inequalities for high-dimensional linear processes with dependent innovations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929548005736448 |
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| author | Mendes, Eduardo Fonseca Lopes, Fellipe |
| author_facet | Mendes, Eduardo Fonseca Lopes, Fellipe |
| contents | We develop concentration inequalities for the $l_\infty$ norm of vector linear processes with sub-Weibull, mixingale innovations. This inequality is used to obtain a concentration bound for the maximum entrywise norm of the lag-$h$ autocovariance matrix of linear processes. We apply these inequalities to sparse estimation of large-dimensional VAR(p) systems and heterocedasticity and autocorrelation consistent (HAC) high-dimensional covariance estimation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_12395 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Concentration inequalities for high-dimensional linear processes with dependent innovations Mendes, Eduardo Fonseca Lopes, Fellipe Statistics Theory Methodology Machine Learning 62M10 We develop concentration inequalities for the $l_\infty$ norm of vector linear processes with sub-Weibull, mixingale innovations. This inequality is used to obtain a concentration bound for the maximum entrywise norm of the lag-$h$ autocovariance matrix of linear processes. We apply these inequalities to sparse estimation of large-dimensional VAR(p) systems and heterocedasticity and autocorrelation consistent (HAC) high-dimensional covariance estimation. |
| title | Concentration inequalities for high-dimensional linear processes with dependent innovations |
| topic | Statistics Theory Methodology Machine Learning 62M10 |
| url | https://arxiv.org/abs/2307.12395 |