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Some equivalences in linear estimation (in Russian)


  • Dmitry Danilov

    (Eindhoven University of Technology, Netherlands)

  • Jan R. Magnus

    (Tilburg University, Netherlands)


Under normality, the Bayesian estimation problem, the best linear unbiased estimation problem, and the restricted least-squares problem are all equivalent. As a result we need not compute pseudo-inverses and other complicated functions, which will be impossible for large sparse systems. Instead, by reorganizing the inputs, we can rewrite the system as a new but equivalent system which can be solved by ordinary least-squares methods.

Suggested Citation

  • Dmitry Danilov & Jan R. Magnus, 2007. "Some equivalences in linear estimation (in Russian)," Quantile, Quantile, issue 3, pages 83-90, September.
  • Handle: RePEc:qnt:quantl:y:2007:i:3:p:83-90

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    Cited by:

    1. Danilov, Dmitry & Magnus, Jan R., 2008. "On the estimation of a large sparse Bayesian system: The Snaer program," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4203-4224, May.
    2. Temel, Tugrul, 2011. "Estimation of a system of national accounts: implementation with mathematica," MPRA Paper 35446, University Library of Munich, Germany.

    More about this item


    Linear Bayes estimation; best linear unbiased; least squares; sparse problems; large-scale optimization;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques


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