Importance Sampling for the Extremal Eigenvalue of $β$-Jacobi ensemble
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909325690142720 |
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| author | Ma, Yutao Wang, Siyu |
| author_facet | Ma, Yutao Wang, Siyu |
| contents | This paper focuses on rare events associated with the tail probabilities of the extremal eigenvalues in the $β$-Jacobi ensemble, which plays a critical role in both multivariate statistical analysis and statistical physics. Under the ultra-high dimensional setting, we give an exact approximation for the tail probabilities and construct an efficient estimator for the tail probabilities. Additionally, we conduct a numerical study to evaluate the practical performance of our algorithms. The simulation results demonstrate that our method offers an efficient and accurate approach for evaluating tail probabilities in practice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16873 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Importance Sampling for the Extremal Eigenvalue of $β$-Jacobi ensemble Ma, Yutao Wang, Siyu Probability This paper focuses on rare events associated with the tail probabilities of the extremal eigenvalues in the $β$-Jacobi ensemble, which plays a critical role in both multivariate statistical analysis and statistical physics. Under the ultra-high dimensional setting, we give an exact approximation for the tail probabilities and construct an efficient estimator for the tail probabilities. Additionally, we conduct a numerical study to evaluate the practical performance of our algorithms. The simulation results demonstrate that our method offers an efficient and accurate approach for evaluating tail probabilities in practice. |
| title | Importance Sampling for the Extremal Eigenvalue of $β$-Jacobi ensemble |
| topic | Probability |
| url | https://arxiv.org/abs/2409.16873 |