Statistical Papers

, Volume 39, Issue 1, pp 109–118 | Cite as

Bayesian estimation of the linear regression model with an uncertain interval constraint on coefficients

  • Alan T. K. Wan
  • William E. Griffiths


This article considers Bayesian inference in the interval constrained normal linear regression model. Whereas much of the previous literature has concentrated on the case where the prior constraint is correctly specified, our framework explicitly allows for the possibility of an invalid constraint. We adopt a non-informative prior and uncertainty concerning the interval restriction is represented by two prior odds ratios. The sampling theoretic risk of the resulting Bayesian interval pre-test estimator is derived, illustrated and explored.


Linear Regression Model Inequality Constraint Risk Function Prior Constraint Sampling Theory 
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. Davis, W.W. (1978), “Bayesian analysis of the linear model subject to linear inequality constraints”,J. Amer. Statist. Assoc. 73, 573–579.MATHCrossRefMathSciNetGoogle Scholar
  2. Escobar, L.A. and Skarpness, B. (1986), “The bias of the least squares estimator over interval constraints”,Econom. Lett. 20, 331–335.CrossRefMathSciNetGoogle Scholar
  3. Escobar, L.A. and Skarpness, B. (1987), “Mean square error and efficiency of the least squares estimator over interval constraints”,Comm. Statist. A— Theory Methods 16, 397–406.MATHCrossRefMathSciNetGoogle Scholar
  4. Gelfand, A.E., Smith, A.F.M. and Lee, T.M. (1992), “Bayesian analysis of constrained parameter and truncated data problems using Gibbs sampling”,J. Amer. Statist. Assoc. 87, 523–532.CrossRefMathSciNetGoogle Scholar
  5. Geweke, J. (1986), “Exact inference in the inequality constrained normal linear regression model”,J. Appl. Econometrics 1, 127–141.CrossRefGoogle Scholar
  6. Griffiths, W.E. (1989), “Bayesian Econometrics and how to get rid of the wrong signs”,Rev. Marketing Agricu. Econom. 56, 36–56.Google Scholar
  7. Griffiths, W.E. and Wan, A.T.K. (1994), “A Bayesian estimator of the linear regression model with an uncertain inequality constraint”, Discussion Paper No. 74, Department of Econometrics, University of New England, Australia.Google Scholar
  8. Hasegawa, H. (1989), “Bayesian estimator of the linear regression model with an interval constraint on coefficients”,Econom. Lett. 31, 9–12.CrossRefMathSciNetGoogle Scholar
  9. Hasegawa, H. (1991), “The MSE of a pre-test estimator of the linear regression model with an interval constraint on coefficients”,J. Japan Statist. Soc. 21, 189–195.MathSciNetGoogle Scholar
  10. Judge, G.G. and Yancey, T.A. (1981), “Sampling properties of an inequality restricted estimator”,Econom. Lett. 7, 327–333.CrossRefMathSciNetGoogle Scholar
  11. Ohtani, K. (1987), “The MSE of least squares estimator over an interval constraint”,Econom. Lett. 25, 351–354.CrossRefMathSciNetGoogle Scholar
  12. Srivastava, V.K. and Ohtani, K. (1995), “A comparison of interval constrained least squares and mixed regression estimator”,Comm. Statist. A—Theory Methods 24, 395–413.MATHCrossRefMathSciNetGoogle Scholar
  13. Wan, A.T.K. (1994), “The non-optimality of the interval restricted and pre-test estimators under squared error loss”,Comm. Statist. A—Theory Methods 23, 2231–2252.MATHCrossRefGoogle Scholar
  14. Wan, A.T.K. (1995), “The optimal critical value of a pre-test for an inequality restriction in a mis-specified regression model”,Austral. J. Statist. 37, 73–82.MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Alan T. K. Wan
    • 1
  • William E. Griffiths
    • 2
  1. 1.Department of Applied Statistics and Operational ResearchCity University of Hong KongKowloonHong Kong
  2. 2.Department of EconometricsUniversity of New EnglandArmidaleAustralia

Personalised recommendations