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All of the non-parametric tests I learned about involved bootstrapping, simulation of large samples of some random variable, or permutation tests. Are there non-parametric tests without simulation or bootstrapping? Do any parametric methods used bootstrapping, generation and simulation of random variables, or permutation tests?

Are all permutations tests or bootstrapping non-parametric?

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  • $\begingroup$ There is something called parametric bootstrap (basically you are sampling the residuals). $\endgroup$ – Maarten Buis Dec 16 '19 at 18:10
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The Wikipedia page on nonparametric statistics lists over 20 common nonparametric statistical tests, most of which do not involve permutation testing or bootstrapping. These tests were generally developed long before modern computational capabilities made bootstrapping and permutation testing realistically possible and even before the relatively recent development of the bootstrap principle.

These tests typically involve statistics whose distributions do not depend on the underlying probability distributions of the values that are being sampled. Some are based, for example, on comparing the ranks of the observations between 2 sets of observations rather than the values themselves. Other tests take advantage of how order statistics translate an ordered set of observations into an estimate of the underlying cumulative probability distribution. Then tests are done along the cumulative probability axis, based on the order statistics of a uniform probability distribution over [0,1], rather than on the observed data directly.

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