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Biometrika 1975 62(2):461-466; doi:10.1093/biomet/62.2.461
© 1975 by Biometrika Trust
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An inequality with application to multivariate analysis

C. M. THEOBALD *

School of Mathematics, University of Bath Avon

An inequality for the trace of the product of two symmetric matrices can be used to simplify the proofs of a number of results in multivariate analysis. This is illustrated on two problems: estimating the parametere of a multivariate normal population, and estimating a system of linear functional relationships between the mean vectors of k multivariate normal populations with the same dispersion matrix. A new result is proved for the corresponding structural relationship problem.

Key Words: Inequality • Linear functional relationship • Linear structural relationship • Matrix trace • Maximum likelihood estimation • Multivariate normal distribution


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