Finite-sample analytic properties of percentile bootstrap intervals

Weizhen Wang (), Chongxiu Yu () and Zhongzhan Zhang ()
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Weizhen Wang: Beijing University of Technology
Chongxiu Yu: Beijing University of Technology
Zhongzhan Zhang: Beijing University of Technology

Metrika: International Journal for Theoretical and Applied Statistics, 2025, vol. 88, issue 6, No 26, 1367-1393

Abstract: Abstract The bootstrap interval is an efficient procedure to estimate parameters. The coverage probability and expected length are crucial to evaluate the reliability and accuracy of a confidence interval. How to compute them for a bootstrap interval at a given parameter configuration for a fixed sample size? In this paper, we offer the first attempt at computing the two quantities of percentile bootstrap intervals by exact probabilistic calculation. This method is applied to ten basic bootstrap intervals for six important parameters. Interestingly, we find that some $$1-\alpha $$ 1 - α bootstrap intervals are narrower than the optimal $$1-\alpha $$ 1 - α z-interval or t-interval.

Keywords: Binomial distribution; Coverage probability; Expected length; Linear model; Normal distribution (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00184-025-00990-8

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