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arXiv · 2402.09397

On the Assessment of Bootstrap Intervals for Samples of Fixed Size

Weizhen Wang·Chongxiu Yu·Zhongzhan Zhang
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Abstract

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.

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Weizhen Wang, Chongxiu Yu, Zhongzhan Zhang. 2024-02-14. On the Assessment of Bootstrap Intervals for Samples of Fixed Size. https://arxiv.org/abs/2402.09397

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