On Linear Estimation Theory for an Infinite Number of Observations

1961 ◽  
Vol 6 (2) ◽  
pp. 166-177 ◽  
Author(s):  
J. Hájek
1991 ◽  
Vol 7 (3) ◽  
pp. 397-403 ◽  
Author(s):  
Kenneth Nordström

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.


1990 ◽  
Vol 29 (5) ◽  
pp. 658 ◽  
Author(s):  
Warren E. Smith ◽  
William J. Dallas ◽  
Walter H. Kullmann ◽  
Heidi A. Schlitt

2020 ◽  
Vol 43 ◽  
Author(s):  
Aba Szollosi ◽  
Ben R. Newell

Abstract The purpose of human cognition depends on the problem people try to solve. Defining the purpose is difficult, because people seem capable of representing problems in an infinite number of ways. The way in which the function of cognition develops needs to be central to our theories.


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