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Best affine unbiased response decomposition

Author

Listed:
  • Dhaene, Geert
  • Schokkaert, Erik
  • Van de Voorde, Carine

Abstract

Given two linear regression models y1=X1[beta]1+u1 and y2=X2[beta]2+u2 where the response vectors y1 and y2 are unobservable but the sum y=y1+y2 is observable, we study the problem of decomposing y into components and , intended to be close to y1 and y2, 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.

Suggested Citation

  • Dhaene, Geert & Schokkaert, Erik & Van de Voorde, Carine, 2003. "Best affine unbiased response decomposition," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 242-253, August.
    • Handle: RePEc:eee:jmvana:v:86:y:2003:i:2:p:242-253
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    References listed on IDEAS

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    1. Neudecker, Heinz, 1977. "Abrahamse and Koerts' 'new estimator' of disturbances in regression analysis," Journal of Econometrics, Elsevier, vol. 5(1), pages 129-133, January.
    2. Erik Schokkaert & Geert Dhaene & Carine Van De Voorde, 1998. "Risk adjustment and the trade‐off between efficiency and risk selection: an application of the theory of fair compensation," Health Economics, John Wiley & Sons, Ltd., vol. 7(5), pages 465-480, August.
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    Cited by:

    1. D. Van den Poel, 2003. "Predicting Mail-Order Repeat Buying. Which Variables Matter?," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(3), pages 371-404.
    2. Haupt, Harry & Oberhofer, Walter, 2005. "Stochastic response restrictions," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 66-75, July.

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