Skip to main content
Log in

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

  • Notes
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Davis, W.W. (1978), “Bayesian analysis of the linear model subject to linear inequality constraints”,J. Amer. Statist. Assoc. 73, 573–579.

    Article  MATH  MathSciNet  Google Scholar 

  • Escobar, L.A. and Skarpness, B. (1986), “The bias of the least squares estimator over interval constraints”,Econom. Lett. 20, 331–335.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  MATH  MathSciNet  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • Geweke, J. (1986), “Exact inference in the inequality constrained normal linear regression model”,J. Appl. Econometrics 1, 127–141.

    Article  Google Scholar 

  • Griffiths, W.E. (1989), “Bayesian Econometrics and how to get rid of the wrong signs”,Rev. Marketing Agricu. Econom. 56, 36–56.

    Google Scholar 

  • 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 

  • Hasegawa, H. (1989), “Bayesian estimator of the linear regression model with an interval constraint on coefficients”,Econom. Lett. 31, 9–12.

    Article  MathSciNet  Google Scholar 

  • 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.

    MathSciNet  Google Scholar 

  • Judge, G.G. and Yancey, T.A. (1981), “Sampling properties of an inequality restricted estimator”,Econom. Lett. 7, 327–333.

    Article  MathSciNet  Google Scholar 

  • Ohtani, K. (1987), “The MSE of least squares estimator over an interval constraint”,Econom. Lett. 25, 351–354.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  MATH  MathSciNet  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The authors are grateful to the editor and the referee for their helpful comments.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wan, A.T.K., Griffiths, W.E. Bayesian estimation of the linear regression model with an uncertain interval constraint on coefficients. Statistical Papers 39, 109–118 (1998). https://doi.org/10.1007/BF02925376

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02925376

Keywords

Navigation