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ENH: add UMPT equivalence test to for some cases

Open josef-pkt opened this issue 2 years ago • 1 comments

I have ignored so far (uniformly most powerful) UMP tests for equivalence and only implemented TOST.

I finally think that we should add them for some easier cases. Add new function equivalence_xxx that selects between UMPT and TOST where TOST is default and delegates to the tost_xxx functions.

related, we might also want UMPT version of nonequivvalence, minimum effect tests.

Wellek's book has large parts for UMP equivalence tests but I did not look at those.

current motivation #8261 umpt and tost for comparing variances Jan and Shieh 2022 use it based of F-test which is nonrobust to nonnormality of the data. But we should be able to get it for the robust versions like Benett.

Jan, Show-Li, and Gwowen Shieh. 2022. “A Comparative Study of TOST and UMPT Procedures for Evaluating Dispersion Equivalence.” Statistics in Biopharmaceutical Research 14 (2): 162–67. https://doi.org/10.1080/19466315.2020.1821762.

AFAIU UMPT are much less popular in applied work than TOST, and can have some nonintuitive non-monotonicities

josef-pkt avatar May 12 '22 19:05 josef-pkt

aside: UMPT for two-sided hypothesis don't exist in general, but for LEF (one parameter ?, Lehmann ?) they do exist.
(I need to find reference again and check more details for which cases UMPT is available.)

josef-pkt avatar May 12 '22 21:05 josef-pkt