Journal of multivariate analysis vol:86 issue:2 pages:242-253
Given two linear regression models y(1) = X(1)beta(1) + u(1) and y(2) = X(2)beta(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) over cap (1) and (y) over cap (2), intended to be close to (y) over cap (1) and (y) over cap (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. (C) 2003 Elsevier Science (USA). All rights reserved.