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The Concentration Ellipsoid of a RandomVector Revisited

Published online by Cambridge University Press:  11 February 2009

Kenneth Nordström
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Abstract

Alternative definitions of the concentration ellipsoidof a random vector are surveyed, and an extension ofthe concentration ellipsoid of Darmois is suggestedas being the most convenient and natural definition.The advantage of the proposed definition inproviding substantially simplified proofs of resultsin (linear) estimation theory is discussed, and isillustrated by new and short proofs of two keyresults. A not-so-well-known, but elementary,extremal representation of a nonnegative definitequadratic form, together with the correspondingCauchy-Schwarẓ-type inequality, is seen to play acrucial role in these proofs.

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Type
Brief Report
Information
Econometric Theory , Volume 7 , Issue 3 , September 1991 , pp. 397 - 403
Copyright
Copyright © Cambridge University Press 1991

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References

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