A note on optimality of hypothesis testing

Commonly, in accordance with a given risk-function of hypothesis testing, investigators try to derive an optimal property of a test. This paper demonstrates that criteria for which a given test is optimal can be declared by the structure of this test, and hence almost any reasonable test is optimal. In order to establish this conclusion, the principle idea of the fundamental lemma of Neyman and Pearson is applied to interpret the goodness of tests, as well as retrospective and sequential change point detections are considered in the context of the proposed technique.Aside from that, the present article evaluates a specific classification problem that corresponds to measurement error effects in occupational medicine.