A characterization of translation-invariant experiments admitting adaptive estimates
The paper under review completely solves the problem of adaptivity for translation invariant experiments. Recall that an estimator for a parameter t is called adaptive if it ignores a nuisance parameter u of the model without loss in efficiency compared with those procedures where u is known. It is pointed out that by definition adaptivity depends on the underlying loss function which determines the minimax risk. In contrast to the common believe, ``independence of t and u'', i.e. \(P_{t,u}=P_ t\otimes P_ u\), is not responsable for adaptivity. It is shown that the existence of independent posterior distributions is equivalent to the adaptivity property. Three types of limit experiments are discussed: local asymptotic (mixed) normal experiments, and experiments arising from densities with jumps.
existence of independent posterior distributions
local asymptotic (mixed) normal experiments
scientific article; zbMATH DE number 4062359
scientific article