Editing Statistical hypothesis test (section)

==Nonparametric bootstrap hypothesis testing==
{{main|Bootstrapping (statistics)}}

Bootstrap-based [[Resampling (statistics)|resampling]] methods can be used for null hypothesis testing. A bootstrap creates numerous simulated samples by randomly resampling (with replacement) the original, combined sample data, assuming the null hypothesis is correct. The bootstrap is very versatile as it is distribution-free and it does not rely on restrictive parametric assumptions, but rather on empirical approximate methods with asymptotic guarantees. Traditional parametric hypothesis tests are more computationally efficient but make stronger structural assumptions. In situations where computing the probability of the test statistic under the null hypothesis is hard or impossible (due to perhaps inconvenience or lack of knowledge of the underlying distribution), the bootstrap offers a viable method for statistical inference.<ref>Hall, P. and Wilson, S.R., 1991. Two guidelines for bootstrap hypothesis testing. Biometrics, pp.757-762.
</ref><ref>Tibshirani, R.J. and Efron, B., 1993. An introduction to the bootstrap. Monographs on statistics and applied probability, 57(1).
</ref><ref>Martin, M.A., 2007. Bootstrap hypothesis testing for some common statistical problems: A critical evaluation of size and power properties. Computational Statistics & Data Analysis, 51(12), pp.6321-6342.
</ref><ref>Horowitz, J.L., 2019. Bootstrap methods in econometrics. Annual Review of Economics, 11, pp.193-224.
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