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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(1-\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>-</mo> <mi>α</mi> </mrow> </math></EquationSource> </InlineEquation> bootstrap intervals are narrower than the optimal <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(1-\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>-</mo> <mi>α</mi> </mrow> </math></EquationSource> </InlineEquation> <i>z</i>-interval or <i>t</i>-interval.</p>

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Finite-sample analytic properties of percentile bootstrap intervals

  • 期刊论文

  • 发表日期：

    2025年2月27日

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  • Weizhen Wang,
  • Chongxiu Yu,
  • Zhongzhan Zhang

摘要

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.