Testing hypotheses by using optimal statistical criteria. I - Kuk, Yu. V.; Petunin, Yu. I. (Ukrains’kyi Matematychnyi Zhurnal, 1994)
We propose a method for constructing statistical criteria. It can be used for testing an arbitrary finite set of simple alternative hypotheses. A concept of an optimal statistical criterion is introduced, special cases of which are the Bayesian criterion and the minimax criterion. It is proved that any optimal statistical criterion can be constructed on the basis of the likelihood ratio.