Tests for the mean of high-dimensional data
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909047093985280 |
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| author | Ferger, Dietmar |
| author_facet | Ferger, Dietmar |
| contents | We consider the problem of testing the mean of high-dimensional data when the dimension may grow without explicit rate restrictions relative to the sample size. The proposed procedure is based on the statistic V_n = n||Xn||^2, which avoids inversion of the covariance matrix and is therefore suitable for high-dimensional settings.We establish asymptotic distributional results for both fixed and increasing dimension by embedding the observations into the Hilbert space l2. Furthermore, we prove the asymptotic validity of a bootstrap approximation for the distribution of the test statistic. The resulting bootstrap test yields asymptotic level-a procedures without requiring sparsity assumptions or structural conditions on the covariance matrix. In all this, a new Central Limit Theorem in l2 is proving to be an extremely useful tool. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_16033 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tests for the mean of high-dimensional data Ferger, Dietmar Statistics Theory 62H15, 62G09, 60F05, 60B12, 62E20 We consider the problem of testing the mean of high-dimensional data when the dimension may grow without explicit rate restrictions relative to the sample size. The proposed procedure is based on the statistic V_n = n||Xn||^2, which avoids inversion of the covariance matrix and is therefore suitable for high-dimensional settings.We establish asymptotic distributional results for both fixed and increasing dimension by embedding the observations into the Hilbert space l2. Furthermore, we prove the asymptotic validity of a bootstrap approximation for the distribution of the test statistic. The resulting bootstrap test yields asymptotic level-a procedures without requiring sparsity assumptions or structural conditions on the covariance matrix. In all this, a new Central Limit Theorem in l2 is proving to be an extremely useful tool. |
| title | Tests for the mean of high-dimensional data |
| topic | Statistics Theory 62H15, 62G09, 60F05, 60B12, 62E20 |
| url | https://arxiv.org/abs/2605.16033 |