On the Theory of Unbiased Tests of Simple Statistical Hypotheses Specifying the Values of Two or More Parameters

Abstract

Unbiased critical regions of type D for testing simple hypotheses specifying the values of several parameters are defined and their properties studied. These regions constitute a natural generalization of the Neyman-Pearson regions of type A for testing simple hypotheses specifying the value of one parameter. A theorem is obtained which plays the role of the Neyman-Pearson fundamental lemma in the type A case. Illustrative examples of type D regions are given.