Adaptive L-statistics for high dimensional test problem
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909354149543936 |
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| author | Ma, Huifang Feng, Long Wang, Zhaojun |
| author_facet | Ma, Huifang Feng, Long Wang, Zhaojun |
| contents | In this study, we focus on applying L-statistics to the high-dimensional one-sample location test problem. Intuitively, an L-statistic with $k$ parameters tends to perform optimally when the sparsity level of the alternative hypothesis matches $k$. We begin by deriving the limiting distributions for both L-statistics with fixed parameters and those with diverging parameters. To ensure robustness across varying sparsity levels of alternative hypotheses, we first establish the asymptotic independence between L-statistics with fixed and diverging parameters. Building on this, we propose a Cauchy combination test that integrates L-statistics with different parameters. Both simulation results and real-data applications highlight the advantages of our proposed methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14308 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adaptive L-statistics for high dimensional test problem Ma, Huifang Feng, Long Wang, Zhaojun Methodology Statistics Theory In this study, we focus on applying L-statistics to the high-dimensional one-sample location test problem. Intuitively, an L-statistic with $k$ parameters tends to perform optimally when the sparsity level of the alternative hypothesis matches $k$. We begin by deriving the limiting distributions for both L-statistics with fixed parameters and those with diverging parameters. To ensure robustness across varying sparsity levels of alternative hypotheses, we first establish the asymptotic independence between L-statistics with fixed and diverging parameters. Building on this, we propose a Cauchy combination test that integrates L-statistics with different parameters. Both simulation results and real-data applications highlight the advantages of our proposed methods. |
| title | Adaptive L-statistics for high dimensional test problem |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2410.14308 |