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.

中文翻译：

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协变量均值的不变检验的可接受性

对于具有p维均值向量θ和任意未知离散矩阵Σ的多重正态分布，Rao（[8]，[9]）针对测试H ₀的问题提出了两种测试：θ ₁ = 0、θ ₂ = 0，Σ未指定，相对于H ₁：θ ₁ ≠ 0，θ ₂ = 0，Σ未指定。这些检验分别称为 Rao 的W检验和 Rao 的U检验。本文证明Rao 的U检验是可接受的，而Hotelling 的T ²检验是不可接受的。