Linear Estimation in Static Systems

2003 ◽  
pp. 121-177 ◽  
Keyword(s):  
Linear Estimation ◽  
Static Systems

Note on Selection of Coordinate Systems for Geodynamics

1975 ◽  
Vol 26 ◽  
pp. 395-407
Author(s):  
S. Henriksen
Keyword(s):  
Sea Level ◽  
The Other ◽  
Coordinate Systems ◽  
Mean Sea Level ◽  
The Earth ◽  
The One ◽  
Static Systems ◽  
Selection Of

The first question to be answered, in seeking coordinate systems for geodynamics, is: what is geodynamics? The answer is, of course, that geodynamics is that part of geophysics which is concerned with movements of the Earth, as opposed to geostatics which is the physics of the stationary Earth. But as far as we know, there is no stationary Earth – epur sic monere. So geodynamics is actually coextensive with geophysics, and coordinate systems suitable for the one should be suitable for the other. At the present time, there are not many coordinate systems, if any, that can be identified with a static Earth. Certainly the only coordinate of aeronomic (atmospheric) interest is the height, and this is usually either as geodynamic height or as pressure. In oceanology, the most important coordinate is depth, and this, like heights in the atmosphere, is expressed as metric depth from mean sea level, as geodynamic depth, or as pressure. Only for the earth do we find “static” systems in use, ana even here there is real question as to whether the systems are dynamic or static. So it would seem that our answer to the question, of what kind, of coordinate systems are we seeking, must be that we are looking for the same systems as are used in geophysics, and these systems are dynamic in nature already – that is, their definition involvestime.

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.

Functional data: local linear estimation of the conditional density and its application

Statistics ◽  
2013 ◽  
Vol 47 (1) ◽  
pp. 26-44 ◽  
Author(s):  
Jacques Demongeot ◽  
Ali Laksaci ◽  
Fethi Madani ◽  
Mustapha Rachdi
Keyword(s):  
Functional Data ◽  
Conditional Density ◽  
Linear Estimation ◽  
Local Linear ◽  
Local Linear Estimation
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