Quantifying Uncertainty: All We Need is the Bootstrap?

2024-03-29

AI Summary

This paper addresses the complexity and high pedagogical/practical barriers associated with conventional uncertainty quantification methods—such as standard errors, confidence intervals, and hypothesis tests—in statistical inference. To evaluate the potential of nonparametric bootstrap as a unified alternative, we conduct a large-scale simulation study rigorously comparing single bootstrap, double bootstrap, and classical methods across multiple dimensions: sample size, confidence level, data-generating mechanisms, and statistical functionals. Results demonstrate that the double bootstrap consistently achieves superior coverage accuracy, stability, and robustness—particularly under small-sample and non-normal conditions—outperforming both classical approaches and the single bootstrap. We thus establish the double bootstrap as a principled, parsimonious, and high-performance paradigm for uncertainty quantification, providing both theoretical justification and empirical evidence to support its adoption in statistical education and applied practice.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

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.

Problem

• Evaluating bootstrap as universal alternative for uncertainty quantification methods
• Comparing double bootstrap performance against traditional confidence interval techniques
• Assessing bootstrap's potential to simplify statistical education and practice

Innovation

• Double bootstrap outperforms BCa method
• Non-parametric bootstrap simplifies statistical estimation
• Double bootstrap consistently performs best overall