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Finite-sample analytic properties of percentile bootstrap intervals

Author

Listed:
  • Weizhen Wang

    (Beijing University of Technology
    Wright State University)

  • Chongxiu Yu

    (Beijing University of Technology)

  • Zhongzhan Zhang

    (Beijing University of Technology)

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.

Suggested Citation

  • Weizhen Wang & Chongxiu Yu & Zhongzhan Zhang, 2025. "Finite-sample analytic properties of percentile bootstrap intervals," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(6), pages 1367-1393, August.
    • Handle: RePEc:spr:metrik:v:88:y:2025:i:6:d:10.1007_s00184-025-00990-8
    DOI: 10.1007/s00184-025-00990-8
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