Testing of coarsening mechanisms: Coarsening at random versus subgroup independence

Abstract Since coarse(ned) data naturally induce set-valued estimators, analysts often assume coarsening at random (CAR) to force them to be single-valued. Using the PASS data as an example, we re-illustrate the impossibility to test CAR and contrast it to another type of uninformative coarsening called subgroup independence (SI). It turns out that SI is testable