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Admissibility of Invariant Tests for Means with Covariates

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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.

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Acknowledgments

The author is grateful to Professor C. R. Rao for his helpful comments. The author would also like to thank an anonymous referee and an associate editor for valuable comments that have led to an improved presentation of the paper.

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  1. Inst. of Statist. Sci., Academia Sinica, Taipei, Taiwan, Republic of China

    Ming-Tien Tsai

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  1. Ming-Tien Tsai
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Correspondence to Ming-Tien Tsai.

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Tsai, MT. Admissibility of Invariant Tests for Means with Covariates. Math. Meth. Stat. 28, 243–261 (2019). https://doi.org/10.3103/S106653071904001X

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  • DOI: https://doi.org/10.3103/S106653071904001X

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