STABILITY OF TESTING HYPOTHESES

The stability of testing hypotheses is discussed. Differing from the u sual tests measured by Neyman-Pearson lemma, the regret and correction of the tests are considered. After the decision is made based on the observations X-1, X-2,..., X-n, one more piece of datum X-n+1 is picke d and the test: is done again in the same way but based on X-1, X-2,.. . X-n, Xn+1. There are three situations: (i) The previous decision is right but the new decision is wrong; (ii) the previous decision is wro ng but the new decision is right; (iii) both of;hem are right or both of them are wrong. Of course, it is desired that the probability of th e occurrence of (i) is as small as possible and the probability of the occurrence of (ii) is as large as possible. Since the sample size is sometimes not chosen very precisely after the type I error and the typ e II error are determined in practice, it seems more urgent to conside r the above problem. Some optimal plans are also given.