Robust estimation for high-dimensional time series with heavy tails
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915009657831424 |
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| author | Wang, Yu Li, Guodong Xiao, Zhijie Xu, Lihu Zhang, Wenyang |
| author_facet | Wang, Yu Li, Guodong Xiao, Zhijie Xu, Lihu Zhang, Wenyang |
| contents | We study in this paper the problem of least absolute deviation (LAD) regression for high-dimensional heavy-tailed time series which have finite $α$-th moment with $α\in (1,2]$. To handle the heavy-tailed dependent data, we propose a Catoni type truncated minimization problem framework and obtain an $\mathcal{O}\big( \big( (d_1+d_2) (d_1\land d_2) \log^2 n / n \big)^{(α- 1)/α} \big)$ order excess risk, where $d_1$ and $d_2$ are the dimensionality and $n$ is the number of samples. We apply our result to study the LAD regression on high-dimensional heavy-tailed vector autoregressive (VAR) process. Simulations for the VAR($p$) model show that our new estimator with truncation are essential because the risk of the classical LAD has a tendency to blow up. We further apply our estimation to the real data and find that ours fits the data better than the classical LAD. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05217 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Robust estimation for high-dimensional time series with heavy tails Wang, Yu Li, Guodong Xiao, Zhijie Xu, Lihu Zhang, Wenyang Statistics Theory We study in this paper the problem of least absolute deviation (LAD) regression for high-dimensional heavy-tailed time series which have finite $α$-th moment with $α\in (1,2]$. To handle the heavy-tailed dependent data, we propose a Catoni type truncated minimization problem framework and obtain an $\mathcal{O}\big( \big( (d_1+d_2) (d_1\land d_2) \log^2 n / n \big)^{(α- 1)/α} \big)$ order excess risk, where $d_1$ and $d_2$ are the dimensionality and $n$ is the number of samples. We apply our result to study the LAD regression on high-dimensional heavy-tailed vector autoregressive (VAR) process. Simulations for the VAR($p$) model show that our new estimator with truncation are essential because the risk of the classical LAD has a tendency to blow up. We further apply our estimation to the real data and find that ours fits the data better than the classical LAD. |
| title | Robust estimation for high-dimensional time series with heavy tails |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2411.05217 |