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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.07429 |
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| _version_ | 1866916357094768640 |
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| author | Pan, Yue Pan, Jiazhu |
| author_facet | Pan, Yue Pan, Jiazhu |
| contents | We obtain the law of large numbers (LLN) and the central limit theorem (CLT) for weakly dependent non-stationary arrays of random fields with asymptotically unbounded moments. The weak dependence condition for arrays of random fields is proved to be inherited through transformation and infinite shift. This paves a way to prove the consistency and asymptotic normality of maximum likelihood estimation for dynamic spatio-temporal models (i.e. so-called ultra high-dimensional time series models) when the sample size and/or dimension go to infinity. Especially the asymptotic properties of estimation for network autoregression are obtained under reasonable regularity conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07429 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Limit Theorems for Weakly Dependent Non-stationary Random Field Arrays and Asymptotic Inference of Dynamic Spatio-temporal Models Pan, Yue Pan, Jiazhu Statistics Theory We obtain the law of large numbers (LLN) and the central limit theorem (CLT) for weakly dependent non-stationary arrays of random fields with asymptotically unbounded moments. The weak dependence condition for arrays of random fields is proved to be inherited through transformation and infinite shift. This paves a way to prove the consistency and asymptotic normality of maximum likelihood estimation for dynamic spatio-temporal models (i.e. so-called ultra high-dimensional time series models) when the sample size and/or dimension go to infinity. Especially the asymptotic properties of estimation for network autoregression are obtained under reasonable regularity conditions. |
| title | Limit Theorems for Weakly Dependent Non-stationary Random Field Arrays and Asymptotic Inference of Dynamic Spatio-temporal Models |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2408.07429 |