Quantifying Uncertainty: All We Need is the Bootstrap?

Abstract: 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.