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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.09397 |
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| _version_ | 1866910331436007424 |
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| author | Wang, Weizhen Yu, Chongxiu Zhang, Zhongzhan |
| author_facet | Wang, Weizhen Yu, Chongxiu Zhang, Zhongzhan |
| contents | A reasonable confidence interval should have a confidence coefficient no less than the given nominal level and a small expected length to reliably and accurately estimate the parameter of interest, and the bootstrap interval is considered to be an efficient interval estimation technique. In this paper, we offer a first attempt at computing the coverage probability and expected length of a parametric or percentile bootstrap interval by exact probabilistic calculation for any fixed sample size. This method is applied to the basic bootstrap intervals for functions of binomial proportions and a normal mean. None of these intervals, however, are found to have a correct confidence coefficient, which leads to illogical conclusions including that the bootstrap interval is narrower than the z-interval when estimating a normal mean. This raises a general question of how to utilize bootstrap intervals appropriately in practice since the sample size is typically fixed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09397 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Assessment of Bootstrap Intervals for Samples of Fixed Size Wang, Weizhen Yu, Chongxiu Zhang, Zhongzhan Statistics Theory Computation A reasonable confidence interval should have a confidence coefficient no less than the given nominal level and a small expected length to reliably and accurately estimate the parameter of interest, and the bootstrap interval is considered to be an efficient interval estimation technique. In this paper, we offer a first attempt at computing the coverage probability and expected length of a parametric or percentile bootstrap interval by exact probabilistic calculation for any fixed sample size. This method is applied to the basic bootstrap intervals for functions of binomial proportions and a normal mean. None of these intervals, however, are found to have a correct confidence coefficient, which leads to illogical conclusions including that the bootstrap interval is narrower than the z-interval when estimating a normal mean. This raises a general question of how to utilize bootstrap intervals appropriately in practice since the sample size is typically fixed. |
| title | On the Assessment of Bootstrap Intervals for Samples of Fixed Size |
| topic | Statistics Theory Computation |
| url | https://arxiv.org/abs/2402.09397 |