Optimal UMP test for parameter in the exponential family

In this paper the problem of testing the one sided hypothesis ₀ in the exponential family against >₀ is considered. By using stopping time, it is pointed out that under certain condition, the resulting test depending on the incomplete data is proved to be equivalent to the UMP test which depends on the full time spans of the instruments. Finally, the optimal stopping time, which generates the UMP test with level and has the minimum total experiment time as well, is obtained.This work is supported in part by the National Natural Science Foundation of China and the Doctoral Program Foundation of China.