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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2510.24182 |
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| _version_ | 1866917047903977472 |
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| author | Rousseau, Judith Rivoirard, Vincent Sulem, Déborah |
| author_facet | Rousseau, Judith Rivoirard, Vincent Sulem, Déborah |
| contents | In this paper we study the frequentist properties of Bayesian approaches in linear high dimensional Hawkes processes in a sparse regime where the number of interaction functions acting on each component of the Hawkes process is much smaller than the dimension. We consider two types of loss function: the empirical $L_1$ distance between the intensity functions of the process and the $L_1$ norm on the parameters (background rates and interaction functions). Our results are the first results to control the $L_1$ norm on the parameters under such a framework. They are also the first results to study Bayesian procedures in high dimensional Hawkes processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24182 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Estimation in linear high dimensional Hawkes processes: a Bayesian approach Rousseau, Judith Rivoirard, Vincent Sulem, Déborah Statistics Theory 62G20 G.3 In this paper we study the frequentist properties of Bayesian approaches in linear high dimensional Hawkes processes in a sparse regime where the number of interaction functions acting on each component of the Hawkes process is much smaller than the dimension. We consider two types of loss function: the empirical $L_1$ distance between the intensity functions of the process and the $L_1$ norm on the parameters (background rates and interaction functions). Our results are the first results to control the $L_1$ norm on the parameters under such a framework. They are also the first results to study Bayesian procedures in high dimensional Hawkes processes. |
| title | Estimation in linear high dimensional Hawkes processes: a Bayesian approach |
| topic | Statistics Theory 62G20 G.3 |
| url | https://arxiv.org/abs/2510.24182 |