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Optimal Estimation in a Linear Regression Model using Incomplete Prior Information

  • Helge Toutenburg
  • Shalabh
  • Christian Heumann

Abstract

For the estimation of regression coefficients in a linear model when incomplete prior information is available, the optimal estimators in the classes of linear heterogeneous and linear homogeneous estimators are considered. As they involve some unknowns, they are operationalized by substituting unbiased estimators for the unknown quantities. The properties of resulting feasible estimators are analyzed and the effect of operationalization is studied. A comparison of the heterogeneous and homogeneous estimation techniques is also presented.

Keywords

Linear Regression Model Risk Function Variance Covariance Matrix Optimal Estimator Multivariate Normal Distribution 
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References

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    Rao, C.R., Toutenburg, H., Shalabh, Heumann, C.: Linear Models and Generalizations: Least Squares and Alternatives (3rd ed.). Springer, New York (2008)MATHGoogle Scholar
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    Theil, H., Goldberger, A.S.: On pure and mixed estimation in econometrics. Int. Econ. Rev. 2, 65–78 (1961)CrossRefGoogle Scholar
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    Toutenburg, H., Trenkler, G., Liski, E.P.: Optimal estimation methods under weakened linear restrictions. Comput. Stat. Data An. 14, 527–536 (1992)CrossRefMathSciNetGoogle Scholar

Copyright information

© Physica-Verlag Heidelberg 2009

Authors and Affiliations

  1. 1.Institut für StatistikUniversität MünchenMünchenGermany
  2. 2.Department of Mathematics & StatisticsIndian Institute of Technology KanpurKanpurIndia

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