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Inference Concerning the Mean Vector When the Covariance Matrix is Totally Reducible

Dennis L. Young
Journal of the American Statistical Association
Vol. 71, No. 355 (Sep., 1976), pp. 696-699
DOI: 10.2307/2285603
Stable URL: http://www.jstor.org/stable/2285603
Page Count: 4
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Inference Concerning the Mean Vector When the Covariance Matrix is Totally Reducible
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Abstract

Given a random sample from a p-variate normal distribution Np(u, Σ), the likelihood ratio criterion and an information theory criterion, which is an analogue of Hotelling's T2, are given for testing H0: u = u0 (known) under the condition that Σ is totally reducible, that is, diagonalizable by an orthogonal matrix which depends upon the pattern but not on the unknown elements of Σ. Exact, approximate and asymptotic distributions of the test criteria are considered and various confidence regions concerning u are provided. Application to repeated measures experiments is discussed.

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