On the extreme order statistics for stationary Gaussian sequences subject to random missing observations
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913377198014464 |
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| author | Fang, Yuan Tan, Zhongquan |
| author_facet | Fang, Yuan Tan, Zhongquan |
| contents | Let $\mathbf{X}=\{X_{n}\}_{n\geq 1}$ be a sequence of stationary Gaussian variables and suppose that only some of the random variables from $\mathbf{X}$ can be observed. In this paper, by studying the limiting properties of multidimensional exceedance point processes for $\mathbf{X}$, we derived the joint limit distribution of extreme order statistics for the Gaussian sequence $\mathbf{X}$ and its observed ones. The joint limit distribution of the locations and heights of the maxima for the Gaussian sequence $\mathbf{X}$ and its observed ones are also obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_13861 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the extreme order statistics for stationary Gaussian sequences subject to random missing observations Fang, Yuan Tan, Zhongquan Probability 60G70, 60G15 Let $\mathbf{X}=\{X_{n}\}_{n\geq 1}$ be a sequence of stationary Gaussian variables and suppose that only some of the random variables from $\mathbf{X}$ can be observed. In this paper, by studying the limiting properties of multidimensional exceedance point processes for $\mathbf{X}$, we derived the joint limit distribution of extreme order statistics for the Gaussian sequence $\mathbf{X}$ and its observed ones. The joint limit distribution of the locations and heights of the maxima for the Gaussian sequence $\mathbf{X}$ and its observed ones are also obtained. |
| title | On the extreme order statistics for stationary Gaussian sequences subject to random missing observations |
| topic | Probability 60G70, 60G15 |
| url | https://arxiv.org/abs/2306.13861 |