Linear estimation theory applied to the reconstruction of a 3-D vector current distribution

1990 ◽  
Vol 29 (5) ◽  
pp. 658 ◽  
Author(s):  
Warren E. Smith ◽  
William J. Dallas ◽  
Walter H. Kullmann ◽  
Heidi A. Schlitt
Keyword(s):  
Current Distribution ◽  
Vector Current ◽  
Estimation Theory ◽  
Linear Estimation

The Concentration Ellipsoid of a Random Vector Revisited

1991 ◽  
Vol 7 (3) ◽  
pp. 397-403 ◽  
Author(s):  
Kenneth Nordström
Keyword(s):  
Quadratic Form ◽  
Random Vector ◽  
Crucial Role ◽  
Type Inequality ◽  
Estimation Theory ◽  
Linear Estimation ◽  
Nonnegative Definite

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.

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