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Balanced Ridge Estimator of Coefficient in Linear Model under a Balanced Loss Function (I)

  • Wenke xu
  • Fengri Li
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 236)

Abstract

Based on the conception of Zellner’s Balanced Loss, considering the goodness of fitting and the accuracy of Ridge Estimator. the paper constructed the balanced loss function and put forward Balanced Ridge estimation of coefficient in linear model, also obtained the property of Balanced Ridge Estimator superior to Least Squares Estimator and admissibility of Balanced Ridge Estimator.

Keywords

Balanced loss function Balanced ridge estimator Ridge estimator Admissibility 

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References

  1. 1.
    Zellner, A.: Bayesian and non-Bayesian estimation using balanced loss functions. In: Gupta, S.S., Berger, J.O. (eds.) Statistical decision theory and related topics V, pp. 377–390. Spring, New York (1994)CrossRefGoogle Scholar
  2. 2.
    Wan, A.T.K.: Risk comparison of inequality constrained least squares and other related estimators under balanced loss. Economics Letters 46, 203–210 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Rodrignes, J., Zellner, A.: Weighted balanced loss function and estimation of the mean time to failure. Communications in Statistics-Theory and Methods 23, 3609–3616 (1994)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Giles, J.A., Giles, D.E.A., ohtani, K.: The exact risk of some pretest and stein-type regression estimators under balanced loss. Communications in Statistics-Theory and Methods 25, 2901–2919 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Xu, X., Wu, Q.: Linear Admissible Estimators of Regression Coefficient Under Balanced Loss. Acta Mathematiea Scientia 20(4), 468–473 (2000)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Luo, H., Bai, C.: The Balanced LS Estimation of the Regressive Coefficient in a Linear Model. Journal of Hunan University (Natural Sciences) 33(2), 122–124 (2006)MathSciNetGoogle Scholar
  7. 7.
    Qiu, H., Luo, J.: Balanced Generalized LS Estimation of the regressive coefficient. Joural of East China Normal University (Natureal Science) (5), 66–71 (2008)Google Scholar
  8. 8.
    Hoerl, A.E., Kennard, R.W.: Ridge Regression: Biased Estimation for Non-orthogonal Problems. Technometrics 12(1), 55–68 (1970)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Wang, S., Shi, J., Yin, S., et al.: Introduction Linear Model, 3rd edn. Science Press, Beijin (2004)Google Scholar
  10. 10.
    Wang, S.: Linear Model Theory and its application. Anhui education Press (1987)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Wenke xu
    • 1
  • Fengri Li
    • 1
  1. 1.College of ScienceNortheast Forestry UniversityP.R. China

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