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The Concentration Ellipsoid of a Random Vector Revisited

Published online by Cambridge University Press:  11 February 2009

Kenneth Nordström
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Abstract

Alternative definitions of the concentration ellipsoid of a random vector are surveyed, and an extension of the concentration ellipsoid of Darmois is suggested as being the most convenient and natural definition. The advantage of the proposed definition in providing substantially simplified proofs of results in (linear) estimation theory is discussed, and is illustrated by new and short proofs of two key results. A not-so-well-known, but elementary, extremal representation of a nonnegative definite quadratic form, together with the corresponding Cauchy-Schwarẓ-type inequality, is seen to play a crucial role in these proofs.

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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