Bootstrapping not under the null?
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908705287569408 |
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| author | Derumigny, Alexis Galanis, Miltiadis Schipper, Wieger van der Vaart, Aad |
| author_facet | Derumigny, Alexis Galanis, Miltiadis Schipper, Wieger van der Vaart, Aad |
| contents | We propose a bootstrap testing framework for a general class of hypothesis tests, which allows resampling under the null hypothesis as well as other forms of bootstrapping. We identify combinations of resampling schemes and bootstrap statistics for which the resulting tests are asymptotically exact and consistent against fixed alternatives. We show that in these cases the limiting local power functions are the same for the different resampling schemes. We also show that certain naive bootstrap schemes do not work. To demonstrate its versatility, we apply the framework to several examples: independence tests, tests on the coefficients in linear regression models, goodness-of-fit tests for general parametric models and for semi-parametric copula models. Simulation results confirm the asymptotic results and suggest that in smaller samples non-traditional bootstrap schemes may have advantages. This bootstrap-based hypothesis testing framework is implemented in the R package BootstrapTests. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_10546 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bootstrapping not under the null? Derumigny, Alexis Galanis, Miltiadis Schipper, Wieger van der Vaart, Aad Statistics Theory Methodology 62F40, 62G10, 62G09, 62F03 (Primary), 62E20 (Secondary) We propose a bootstrap testing framework for a general class of hypothesis tests, which allows resampling under the null hypothesis as well as other forms of bootstrapping. We identify combinations of resampling schemes and bootstrap statistics for which the resulting tests are asymptotically exact and consistent against fixed alternatives. We show that in these cases the limiting local power functions are the same for the different resampling schemes. We also show that certain naive bootstrap schemes do not work. To demonstrate its versatility, we apply the framework to several examples: independence tests, tests on the coefficients in linear regression models, goodness-of-fit tests for general parametric models and for semi-parametric copula models. Simulation results confirm the asymptotic results and suggest that in smaller samples non-traditional bootstrap schemes may have advantages. This bootstrap-based hypothesis testing framework is implemented in the R package BootstrapTests. |
| title | Bootstrapping not under the null? |
| topic | Statistics Theory Methodology 62F40, 62G10, 62G09, 62F03 (Primary), 62E20 (Secondary) |
| url | https://arxiv.org/abs/2512.10546 |