摘要：Suppose that a statistician observes two independent variates X1 and X2 having densities fi(⋅;θ)≡fi(⋅−θ),i=1,2, θ∈R. His purpose is to conduct a test for H:θ=0vs.K:θ∈R∖{0} with a pre-defined significance level α∈(0,1). Moran (1973) suggested a test which is based on a single split of the data, i.e., to use X2 in order to conduct a one-sided test in the direction of X1. Specifically, if b1 and b2 are the (1−α)’th and α’th quantiles associated with the distribution of X2 under H, then Moran’s test has a rejection zone (a,∞)×(b1,∞)∪(−∞,a)×(−∞,b2) where a∈R is a design parameter. Motivated by this issue, the current work includes an analysis of a new notion, regular admissibility of tests. It turns out that the theory regarding this kind of admissibility leads to a simple sufficient condition on f1(⋅) and f2(⋅) under which Moran’s test is inadmissible.
