A characterization of translation-invariant experiments admitting adaptive estimates

Statistical experiments possess the property of adaptivity, if the ignorance of a nuisance parameter does not cause any loss in efficiency. In order to include a large variety of cases, the efficiency is measured in terms of minimax bounds. It is shown that a necessary and sufficient condition for adaptivity of translation invariant experiments is that the parameter of interest and the nuisance parameter are a.s. independent w.r.t. the posterior distributions.