Quantifying uncertainty through standard errors, confidence intervals, hypothesis tests, and related measures is a fundamental aspect of statistical practice. However, these techniques involve a variety of methods, mathematical formulas, and underlying concepts, which can be complex. Could the non-parametric bootstrap, known for its simplicity and general applicability, serve as a universal alternative? In this study, we address this question through a review of existing literature and a simulation analysis of one- and two-sided confidence intervals across varying sample sizes, confidence levels, data-generating processes, and statistical functionals. Our findings indicate that the double bootstrap consistently performs best and is a promising alternative to traditional methods used for common statistical tasks. These results suggest that the bootstrap, particularly the double bootstrap, could simplify statistical education and practice without compromising effectiveness.

翻译：通过标准误差、置信区间、假设检验及相关度量来量化不确定性是统计实践的基本环节。然而，这些技术涉及多种方法、数学公式及潜在概念，可能较为复杂。以简洁性和普适性著称的非参数自举法能否成为通用替代方案？本研究通过文献综述及模拟分析探讨该问题，考察了不同样本量、置信水平、数据生成过程及统计泛函下的单双侧置信区间。研究结果表明，双重自举法始终表现最佳，是常见统计任务传统方法的有力替代方案。这些发现意味着自举法（尤其是双重自举法）可在不影响效能的前提下，显著简化统计学教学与实践。