Goodness-of-fit Tests for Heavy-tailed Random Fields
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911306129342464 |
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| author | Niu, Ying Chen, Zhao Wang, Christina Dan Zhao, Yuwei |
| author_facet | Niu, Ying Chen, Zhao Wang, Christina Dan Zhao, Yuwei |
| contents | We develop goodness-of-fit tests for max-stable random fields, which are used to model heavy-tailed spatial data. The test statistics are constructed based on the Fourier transforms of the indicators of extreme values in the heavy-tailed spatial data, whose asymptotic distribution is a Gaussian random field under a hypothesized max-stable random field. Since the covariance structure of the limiting Gaussian random field lacks an explicit expression, we propose a stationary bootstrap procedure for spatial fields to approximate critical values. Simulation studies confirm the theoretical distributional results, and applications to PM2.5 and temperature data illustrate the practical utility of the proposed method for model assessment. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06412 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Goodness-of-fit Tests for Heavy-tailed Random Fields Niu, Ying Chen, Zhao Wang, Christina Dan Zhao, Yuwei Methodology We develop goodness-of-fit tests for max-stable random fields, which are used to model heavy-tailed spatial data. The test statistics are constructed based on the Fourier transforms of the indicators of extreme values in the heavy-tailed spatial data, whose asymptotic distribution is a Gaussian random field under a hypothesized max-stable random field. Since the covariance structure of the limiting Gaussian random field lacks an explicit expression, we propose a stationary bootstrap procedure for spatial fields to approximate critical values. Simulation studies confirm the theoretical distributional results, and applications to PM2.5 and temperature data illustrate the practical utility of the proposed method for model assessment. |
| title | Goodness-of-fit Tests for Heavy-tailed Random Fields |
| topic | Methodology |
| url | https://arxiv.org/abs/2512.06412 |