Minimax estimation of the structure factor of spatial point processes
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918208237207552 |
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| author | Mastrilli, Gabriel |
| author_facet | Mastrilli, Gabriel |
| contents | We investigate the problem of estimating the structure factor, or spectra, of stationary spatial point processes. In the first part, we establish a minimax lower bound for this estimation problem, using an approach tailored to second-order properties of spatial point processes. Although not the main focus, this methodology also extends naturally to a minimax lower bound for the estimation of the pair correlation function of spatial point processes. In the second part, we construct a multitaper estimator that achieves the optimal rate of convergence in squared risk. Under a Brillinger-mixing condition, we further establish a chi-square-type concentration bound. Finally, we propose a data-driven procedure for selecting the number of tapers, supported by an oracle inequality, and we demonstrate the practical effectiveness of the method through numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14551 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimax estimation of the structure factor of spatial point processes Mastrilli, Gabriel Statistics Theory Primary: 62M15, 62M30, 62G05, Secondary: 62C20, 60G55 We investigate the problem of estimating the structure factor, or spectra, of stationary spatial point processes. In the first part, we establish a minimax lower bound for this estimation problem, using an approach tailored to second-order properties of spatial point processes. Although not the main focus, this methodology also extends naturally to a minimax lower bound for the estimation of the pair correlation function of spatial point processes. In the second part, we construct a multitaper estimator that achieves the optimal rate of convergence in squared risk. Under a Brillinger-mixing condition, we further establish a chi-square-type concentration bound. Finally, we propose a data-driven procedure for selecting the number of tapers, supported by an oracle inequality, and we demonstrate the practical effectiveness of the method through numerical experiments. |
| title | Minimax estimation of the structure factor of spatial point processes |
| topic | Statistics Theory Primary: 62M15, 62M30, 62G05, Secondary: 62C20, 60G55 |
| url | https://arxiv.org/abs/2511.14551 |