Asymptotic justification of the bootstrap often takes the form of weak convergence of the bootstrap distribution to some limit distribution. Theoretical literature recognized that the weak convergence does not imply consistency of the bootstrap second moment or the bootstrap variance as an estimator of the asymptotic variance, but such concern is not always reflected in the applied practice. We bridge the gap between the theory and practice by showing that such common bootstrap based standard error in fact leads to a potentially conservative inference.

中文翻译：

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Bootstrap 标准误差估计和推理

自举的渐近证明通常采用自举分布弱收敛到某个极限分布的形式。理论文献认识到弱收敛并不意味着作为渐近方差估计量的自举二阶矩或自举方差的一致性，但这种关注并不总是反映在应用实践中。我们通过证明这种基于标准错误的常见引导程序实际上会导致潜在的保守推断，从而弥合了理论与实践之间的差距。