In this undergraduate thesis, we develop the bootstrap-inference library for the Python programming language, which provides an extensible implementation of bootstrap inference methods with an emphasis on double-percentile confidence intervals. The library also supports percentile confidence intervals, estimation of bias and variance, user-defined statistics, alternative resampling schemes, parallel execution across multiple CPU cores, and reproducibility of results. We verify the correctness of the implementation of double-percentile confidence intervals through a simulation study in which we compare our implementation with the reference implementation provided by the bootstrap-ci library. Across the considered distributions, statistical functionals, and sample sizes, the two implementations agree closely in terms of coverage probability. We further demonstrate the applicability of the developed library through a simulation study on synthetic hierarchical data, in which we compare the coverage of different confidence interval procedures under violations of the normality assumption for the distribution of random effects. Under departures from normality, the nonparametric percentile method achieves better coverage for the standard deviations of the random effects than the parametric methods. The double bootstrap, however, does not always improve the coverage of the nonparametric percentile method.
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