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Abstract <p>This study aims to investigate the convergence properties of the exact closed-form formula for the distribution of indices in a sorted sample being medians of Poisson-bootstrapped subsamples toward the binomial distribution. We find that although the two distributions do not coincide exactly, their asymptotic behaviors are of the same order, specifically <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(O\left(1/{\sqrt{n}}\right)\)</EquationSource> <!--LobJMat2561350Pile-m1--> </InlineEquation> as the sample size <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(n\)</EquationSource> <!--LobJMat2561350Pile-m2--> </InlineEquation> increases. The findings have significant implications for statistical inference and resampling techniques, as they provide deeper insights into the efficiency and accuracy of the Poisson bootstrap method.</p>

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On Convergence of Different Bootstrap Approximations for Medians

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • I. E. Pile

摘要

Abstract

This study aims to investigate the convergence properties of the exact closed-form formula for the distribution of indices in a sorted sample being medians of Poisson-bootstrapped subsamples toward the binomial distribution. We find that although the two distributions do not coincide exactly, their asymptotic behaviors are of the same order, specifically \(O\left(1/{\sqrt{n}}\right)\) as the sample size \(n\) increases. The findings have significant implications for statistical inference and resampling techniques, as they provide deeper insights into the efficiency and accuracy of the Poisson bootstrap method.