Statistische Hefte

, Volume 26, Issue 1, pp 263–285 | Cite as

An evaluation of biased estimators of regression coefficients—A simulation study

  • M. Precht
  • P. S. S. N. V. P. Rao


Different versions of generalized and ordinary ridge estimators and shrinkage estimators of regression coefficients are studied in comparison with least squares estimators using simulations. The results show that some of the biased estimators considered are better than the least squares estimator in general and the improvement is substantial in some cases.


Mean Square Error Ridge Regression Shrinkage Estimator Ridge Parameter Predictive Mean Square Error 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Dempster, A. P., Schatzoff, M., and Wermuth, N. (1977), “A Simulation Study of Alternatives to Ordinary least-Squares”, Journal of the American Statistical Association, 72, 77–91.MATHCrossRefGoogle Scholar
  2. Efron, B., and Morris, C. (1975), “Data Analysis Using Stein's Estimator and Its Generalizations”, Journal of the American Statistical Association, 70, 311–319.MATHCrossRefGoogle Scholar
  3. Farebrother, R. W. (1975), “The Minimum Mean Square Error Linear Estimator and Ridge Regression”, Technometrics, 17, 122–128.CrossRefMathSciNetGoogle Scholar
  4. Gunst, R. F., and Maso, R. L. (1977), “Biased Estimation in Regression: An Evaluation Using Mean Squared Error”, Journal of the American Statistical Association, 72, 616–628.MATHCrossRefMathSciNetGoogle Scholar
  5. Hemmerle, W. J. (1975), “An Explicit Solution for Generalized Ridge Regression”, Technometrics, 17, 309–314.MATHCrossRefMathSciNetGoogle Scholar
  6. Hemmerle, W. J., and Brantle, T. F. (1978), “Explicit and constrained Generalized Ridge Estimation”, Technometrics, 20, 109–120.MATHCrossRefGoogle Scholar
  7. Hoerl, A. E., and Kennard, R. W. (1970), “Ridge Regression: Biased Estimation of Nonorthogonal Problems”, Technometrics, 12, 55–67.MATHCrossRefGoogle Scholar
  8. Hoerl, A. E., Kennard, R. W. (1970), “Ridge Regression: Applications to Nonorthogonal Problems”, Technometrics, 12, 69–82.MATHCrossRefGoogle Scholar
  9. Hoerl, A. E., Kennard R. W. (1976), “Ridge Regression: Iterative Estimation of the Biasing Parameter”, Communications in Statistics, A 5, 77–88.Google Scholar
  10. Hoerl, A. E., Kennard, R. W., and Baldwin, K. F. (1975), “Ridge Regression: some simulations”, Communications in Statistics, 4, 105–123.CrossRefGoogle Scholar
  11. Lawless, J. F., and Wang, P. (1976), “A Simulation Study of Ridge and Other Regression Estimators”, Communications in Statistics, Ser. A, 5, 307–323.CrossRefGoogle Scholar
  12. Marquardt, D. W., and Snee, R. D. (1975), “Ridge Regression in Practice”, The American Statistician, 29, 3–20.MATHCrossRefGoogle Scholar
  13. Mc Gue, M. K. (1981), “Ridge Regression: Estimation and Prediction” Ph. D. Thesis, University of Minnesota.Google Scholar
  14. Rao, C. R. (1973), “Linear Statistical Inference and Its Applications”, 2nd ed. John Wiley and Sons Inc., New York.MATHGoogle Scholar
  15. Stein, C. (1960), “Multiple Regression”, Constributions to Probability and Statistics. Essays in Honor of Harald Hotelling I, Standford University Press, 424–443.Google Scholar
  16. Theil, H. (1971), “Principles of Econometrics”, John Wiley and Sons Inc., New York.MATHGoogle Scholar
  17. Theobald, C. M. (1974), “Generalizations of Mean Square Error Applied to Ridge Regression”, Journal of the Royal Statistical Society, Series B, 36, 103–106.MATHMathSciNetGoogle Scholar
  18. Trenkler, G. (1981), “On a Generalized Iteration Estimator” Computational Statistics, de Gruyter, Berlin-New York, 315–335.Google Scholar
  19. Vinod, H. D. (1976), “Simulation and Extension of a Minumum Mean Squared Error Estimator in Comparison with Stein's.” Technometrics, 18, 491–496.MATHCrossRefMathSciNetGoogle Scholar
  20. Vinod, H. D. (1977), “Estimating the Largest Acceptable k and a Confidence Interval for Ridge Regression Parameter”, Presented at the Econometric Society European Meeting, Vienna.Google Scholar
  21. Vinod, H. D., and Ullah, A. (1981), “Recent Advances in Regression Methods”, Marcel Dekker, Inc., New York.MATHGoogle Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • M. Precht
    • 1
  • P. S. S. N. V. P. Rao
    • 1
  1. 1.Abt. Mathematik und Statistik Datenverarbeitungsstelle WeihenstephanFreising 12

Personalised recommendations