Statistics Colloquium : Dr. Yehenew Kifle

Abstract: The inferential problem of drawing inference about a common mean of several independent normal populations with unequal variances has drawn universal attention, and there are many exact and asymptotic tests for testing a null hypothesis $H_0:\mu=\mu_0$ against two-sided alternatives. In this talk, I will provide a review of some of these exact and asymptotic tests, and present theoretical expressions of local powers of the exact tests and a comparison. It turns out that, in the case of equal sample size, a uniform comparison and ordering of the exact tests based on their local power can be carried out even when the variances are unknown.