Zk. Zheng, STABILITY OF TESTING HYPOTHESES, Science in China. Series A, Mathematics, Physics, Astronomy & Technological Sciences, 40(9), 1997, pp. 932-944
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.