Best affine unbiased response decomposition

Given two linear regression models y 1= X 1 β 1+ u 1 and y 2= X 2 β 2+ u 2 where the response vectors y 1 and y 2 are unobservable but the sum y= y 1+ y 2 is observable, we study the problem of decomposing y into components y ̂ 1 and y ̂ 2 , intended to be close to y 1 and y 2, respectively. We deve...

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Bibliographic Details
Published in:Journal of multivariate analysis 2003-08, Vol.86 (2), p.242-253
Main Authors: Dhaene, Geert, Schokkaert, Erik, Van de Voorde, Carine
Format: Article
Language:English
Subjects:
Best affine unbiasedness
Decomposability
Decomposability Decomposition of response Best affine unbiasedness Gauss-Markov theory
Decomposition of response
Exact sciences and technology
Gauss–Markov theory
Linear inference, regression
Mathematics
Multivariate analysis
Probability and statistics
Sciences and techniques of general use
Statistics
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Summary:Given two linear regression models y 1= X 1 β 1+ u 1 and y 2= X 2 β 2+ u 2 where the response vectors y 1 and y 2 are unobservable but the sum y= y 1+ y 2 is observable, we study the problem of decomposing y into components y ̂ 1 and y ̂ 2 , intended to be close to y 1 and y 2, respectively. We develop a theory of best affine unbiased decomposition in this setting. A necessary and sufficient condition for the existence of an affine unbiased decomposition is given. Under this condition, we establish the existence and uniqueness of the best affine unbiased decomposition and provide an expression for it.
ISSN:0047-259X
1095-7243
DOI:10.1016/S0047-259X(03)00023-X