Quantifying Uncertainty: All We Need is the Bootstrap?
arxiv(2024)
Abstract
Standard errors, confidence intervals, hypothesis tests, and other
quantifications of uncertainty are essential to statistical practice. However,
they feature a plethora of different methods, mathematical formulas, and
concepts. Could we not just replace them all with the general and relatively
easy-to-understand non-parametric bootstrap? We contribute to answering this
question with a review of related work and a simulation study of one- and
two-sided confidence intervals over several different sample sizes, confidence
levels, data generating processes, and functionals. Results show that double
bootstrap is the overall best method and a viable alternative to typically used
approaches in all but the smallest sample sizes.
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