Is the locally best invariant test uniformly most powerful for a wider class of invariant tests?

In the context of a general regression model in which some regression coefficients are of interest and others are purely nuisance parameters, Bhowmik and King [6] constructed the locally best invariant (LBI) test against one-sided alternatives. This paper investigates whether this LBI test is uniformly most powerful invariant (UMPI) or not through simulation results. A test that is locally best invariant against one-sided alternative hypotheses is found to be uniformly most powerful invariant (UMPI) in a wider class of tests than the invariant tests for the standard F test. The results of a simulation study conducted to prove that the LBI test is UMPI are presented. Through simulation results this study proves that the LBI test is UMPI.