Sub-Gaussian High-Dimensional Covariance Matrix Estimation under Elliptical Factor Model with 2 + εth Moment
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866914849334755328 |
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| author | Ding, Yi Zheng, Xinghua |
| author_facet | Ding, Yi Zheng, Xinghua |
| contents | We study the estimation of high-dimensional covariance matrices under elliptical factor models with 2 + εth moment. For such heavy-tailed data, robust estimators like the Huber-type estimator in Fan, Liu and Wang (2018) can not achieve sub-Gaussian convergence rate. In this paper, we develop an idiosyncratic-projected self-normalization (IPSN) method to remove the effect of heavy-tailed scalar parameter, and propose a robust pilot estimator for the scatter matrix that achieves the sub-Gaussian rate. We further develop an estimator of the covariance matrix and show that it achieves a faster convergence rate than the generic POET estimator in Fan, Liu and Wang (2018). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18347 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sub-Gaussian High-Dimensional Covariance Matrix Estimation under Elliptical Factor Model with 2 + εth Moment Ding, Yi Zheng, Xinghua Statistics Theory We study the estimation of high-dimensional covariance matrices under elliptical factor models with 2 + εth moment. For such heavy-tailed data, robust estimators like the Huber-type estimator in Fan, Liu and Wang (2018) can not achieve sub-Gaussian convergence rate. In this paper, we develop an idiosyncratic-projected self-normalization (IPSN) method to remove the effect of heavy-tailed scalar parameter, and propose a robust pilot estimator for the scatter matrix that achieves the sub-Gaussian rate. We further develop an estimator of the covariance matrix and show that it achieves a faster convergence rate than the generic POET estimator in Fan, Liu and Wang (2018). |
| title | Sub-Gaussian High-Dimensional Covariance Matrix Estimation under Elliptical Factor Model with 2 + εth Moment |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2406.18347 |