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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.14431 |
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| _version_ | 1866912974176780288 |
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| author | Chen, Zengjing Liu, Ruihan Yao, Jianfeng |
| author_facet | Chen, Zengjing Liu, Ruihan Yao, Jianfeng |
| contents | This paper investigates testing for deviation of a high-dimensional mean vector $\boldsymbolμ$. In contrast to the standard one-sample significance test of the form: $H_0^\texttt{e} : \boldsymbolμ = \boldsymbolμ_0$ versus $H_1^\texttt{e} : \boldsymbolμ \neq \boldsymbolμ_0$, we focus on testing the deviation $H_0 : \|\boldsymbolμ - \boldsymbolμ_0\|_2 \ge d_0$ versus $H_1 : \|\boldsymbolμ - \boldsymbolμ_0\|_2 < d_0$ for a prespecified length $d_0 > 0$. Constructing a valid test statistic for this problem is technically nontrivial. By applying the concept of positive and negative feedback processes from control theory, we propose a test statistic based on a two-armed bandit (TAB) process. The deviation test is also extended to the two-sample setting. Simulation experiments confirm a good performance of the tests in finite samples. Finally, a real data analysis demonstrates the practical significance of the proposed deviation tests. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14431 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deviation Tests for a High-dimensional Mean Chen, Zengjing Liu, Ruihan Yao, Jianfeng Methodology This paper investigates testing for deviation of a high-dimensional mean vector $\boldsymbolμ$. In contrast to the standard one-sample significance test of the form: $H_0^\texttt{e} : \boldsymbolμ = \boldsymbolμ_0$ versus $H_1^\texttt{e} : \boldsymbolμ \neq \boldsymbolμ_0$, we focus on testing the deviation $H_0 : \|\boldsymbolμ - \boldsymbolμ_0\|_2 \ge d_0$ versus $H_1 : \|\boldsymbolμ - \boldsymbolμ_0\|_2 < d_0$ for a prespecified length $d_0 > 0$. Constructing a valid test statistic for this problem is technically nontrivial. By applying the concept of positive and negative feedback processes from control theory, we propose a test statistic based on a two-armed bandit (TAB) process. The deviation test is also extended to the two-sample setting. Simulation experiments confirm a good performance of the tests in finite samples. Finally, a real data analysis demonstrates the practical significance of the proposed deviation tests. |
| title | Deviation Tests for a High-dimensional Mean |
| topic | Methodology |
| url | https://arxiv.org/abs/2603.14431 |