Admissibility of Invariant Tests for Means with Covariates

Abstract

For a multinormal distribution with a p-dimensional mean vector θ and an arbitrary unknown dispersion matrix Σ, Rao ([8], [9]) proposed two tests for the problem of testing H₀: θ₁ = 0, θ₂ = 0, Σ unspecified, versus H₁: θ₁ ≠ 0, θ₂ = 0, Σ unspecified. These tests are known as Rao’s W-test and Rao’s U-test, respectively. In this paper, it is shown that Rao’s U-test is admissible while Hotelling’s T²-test is inadmissible.