ENH: permutation tests: transformation versus robust statistics

[josef-pkt]

#6421 nonzero null
several other issues for permutation

I need to collect references

permutation are easy under common distribution assumption, or simple mean-shift assumption, but they can be nonrobust in general unless we want to change our null hypothesis to e.g. brunner-munzel stochastic dominance, instead of comparisons of mean or mean parameters.

e.g. heteroscedasticity

• transform, zscore data before permutation (zscore data and then add mean back in)
• use studentized t-test (Welch) with permutation of original data

searching "studetized permutation" finds the second approach using test statistic designed for or robust to heteroscedasticity

I don't remember where I saw the first approach

Implementation should be easy, but I have no overview which permutation under which assumptions,
I need references that look like good candidates to implement.