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

An efficient algorithm for continuous-discrete linear estimation problems

2001 ◽  
Vol 8 (12) ◽  
pp. 310-312 ◽  
Author(s):  
J. Navarro-Moreno ◽  
J.C. Ruiz-Molina
Keyword(s):  
Efficient Algorithm ◽  
Linear Estimation ◽  
Estimation Problems

Functional data analysis: local linear estimation of the $$L_1$$ L 1 -conditional quantiles

2018 ◽  
Vol 28 (2) ◽  
pp. 217-240 ◽  
Author(s):  
Fahimah A. Al-Awadhi ◽  
Zoulikha Kaid ◽  
Ali Laksaci ◽  
Idir Ouassou ◽  
Mustapha Rachdi
Keyword(s):  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Linear Estimation ◽  
Conditional Quantiles ◽  
Local Linear ◽  
Local Linear Estimation
Sign in / Sign up

Export Citation Format

Share Document