Testing One Hypothesis Multiple Times

In applied settings, tests of hypothesis where a nuisance parameter is only identifiable under the alternative often reduces into one Testing One Hypothesis Multiple times (TOHM). Specifically, fine discretization space non-identifiable specified, and null tested against set sub-alternative hypothesis, for each point discretization. The resulting sub-test statistics are then combined to obtain global p-value. this paper, we discuss computationally efficient inferential tool perform TOHM stringent significance requirements, such as those typically required in physical sciences, (e.g., p-value $<10^{-7}$). procedure leads generalized approach inference non-standard conditions, including non-nested models comparisons.