Inference in linear models with inequality constrained parameters

Henning Knautz

Discussiones Mathematicae Probability and Statistics (2000)

  • Volume: 20, Issue: 1, page 135-161
  • ISSN: 1509-9423

Abstract

top
In many econometric applications there is prior information available for some or all parameters of the underlying model which can be formulated in form of inequality constraints. Procedures which incorporate this prior information promise to lead to improved inference. However careful application seems to be necessary. In this paper we will review some methods proposed in the literature. Among these there are inequality constrained least squares (ICLS), constrained maximum likelihood (CML) and minimax estimation. On the other hand there exists a large variety of Bayesian methods using Monte Carlo integration or Markov Chain Monte Carlo (MCMC) methods The different methods are discussed and some of them are compared by means of a simulation study.

How to cite

top

Henning Knautz. "Inference in linear models with inequality constrained parameters." Discussiones Mathematicae Probability and Statistics 20.1 (2000): 135-161. <http://eudml.org/doc/287655>.

@article{HenningKnautz2000,
abstract = {In many econometric applications there is prior information available for some or all parameters of the underlying model which can be formulated in form of inequality constraints. Procedures which incorporate this prior information promise to lead to improved inference. However careful application seems to be necessary. In this paper we will review some methods proposed in the literature. Among these there are inequality constrained least squares (ICLS), constrained maximum likelihood (CML) and minimax estimation. On the other hand there exists a large variety of Bayesian methods using Monte Carlo integration or Markov Chain Monte Carlo (MCMC) methods The different methods are discussed and some of them are compared by means of a simulation study.},
author = {Henning Knautz},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {inequality constraints; linear regression model; comparison of estimators; Monte Carlo simulation; tables},
language = {eng},
number = {1},
pages = {135-161},
title = {Inference in linear models with inequality constrained parameters},
url = {http://eudml.org/doc/287655},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Henning Knautz
TI - Inference in linear models with inequality constrained parameters
JO - Discussiones Mathematicae Probability and Statistics
PY - 2000
VL - 20
IS - 1
SP - 135
EP - 161
AB - In many econometric applications there is prior information available for some or all parameters of the underlying model which can be formulated in form of inequality constraints. Procedures which incorporate this prior information promise to lead to improved inference. However careful application seems to be necessary. In this paper we will review some methods proposed in the literature. Among these there are inequality constrained least squares (ICLS), constrained maximum likelihood (CML) and minimax estimation. On the other hand there exists a large variety of Bayesian methods using Monte Carlo integration or Markov Chain Monte Carlo (MCMC) methods The different methods are discussed and some of them are compared by means of a simulation study.
LA - eng
KW - inequality constraints; linear regression model; comparison of estimators; Monte Carlo simulation; tables
UR - http://eudml.org/doc/287655
ER -

References

top
  1. [1] G. Box and G. Tiao, Bayesian Inference in Statistical Analysis, New York: Wiley (1973), reprinted in: Wiley Classics Library Edition 1992. Zbl0271.62044
  2. [2] W. Davis, Bayesian analysis of the linear model subject to linear inequality constraints, JASA 73 (363) (1978), 573-579. Zbl0403.62046
  3. [3] J. Geweke, Exact inference in the inequality constrained normal linear regression model, Journal of Applied Econometrics 1 (1986), 127-141. 
  4. [4] J. Geweke, Bayesian inference in econometric models using Monte Carlo integration, Econometrica 57 (6) (1989), 1317-1339. Zbl0683.62068
  5. [5] J. Geweke, Bayesian inference for linear models subject to linear inequality constraints, in: Modelling and Prediction, J. Lee, W. O. Johnson and A. Zellner (eds.), New York, Springer 1996, 248-263. Zbl0895.62028
  6. [6] O.W. Gilley and R. K. Pace, Improving hedonic estimation with an inequality restricted estimator, Review of Economics and Statistics 77 (4) (1995), 609-621. 
  7. [7] C. Gourieroux and A. Monfort, Statistics and Econometric Models, Volume 1+2 Cambridge University Press (1995). Zbl0870.62088
  8. [8] B. Heiligers, Linear Bayes and minimax estimation in linear models withpartially restricted parameter space, Journal of Statistical Planning and Inference 36 (1993), 175-184. 
  9. [9] J. Judge and T. Takayama, Inequality restrictions in regression analysis, Journal of the American Statistical Association 61 (1966), 166-181. Zbl0144.41702
  10. [10] K. Klaczynsk, i On inequality constrained generalized least squares estimation of parameter functions, A case of arbitrary linear restrictions, Discussiones Mathematicae, Algebra and Stochastic Methods 15 (1995), 297-312. Zbl0842.62042
  11. [11] T. Kloek and H.K. Van Dijk, Bayesian estimates of equation system parameters: An application of integration by Monte Carlo, Econometrica 46 (1) (1978), 1-19. Zbl0376.62014
  12. [12] J. Lauterbach and P. Stahlecker, A numerical method for an approximate minimax estimator in linear regression, Linear Algebra and its Applications 176 (1992), 91-108. Zbl0762.65109
  13. [13] C.Liew, Inequality constrained least squares estimation, Journal of the American Statistical Association 71 (1976), 746-751. Zbl0342.62037
  14. [14] D.G. Luenberger, Linear and Nonlinear Programming, (2nd ed.) Addison Wesley 1984. Zbl0571.90051
  15. [15] D. O'Leary and B. Rust, Confidence intervals for inequality-constrained least squares problems, with applications to ill posed problems, SIAM J. Sci. Stat.Comput. 7 (2) (1986), 473-489. Zbl0593.65092
  16. [16] J. Pilz, Bayesian Estimation and Experimental Design in Linear Regression Models, New York: Wiley 1991. Zbl0745.62068
  17. [17] R. Pindyck and D. Rubinfeld, Econometric Models and Forecasts, New York: Wiley. 
  18. [18] R. Schoenberg, Constrained maximum likelihood, Computational Economics 10 (1997), 251-266. Zbl0893.90179
  19. [19] A.F.M. Smith and G. O. Roberts, Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods, Journal of the Royal Statistical Society B 55 (1) (1993), 3-23. Zbl0779.62030
  20. [20] P. Stahlecker and K. Schmidt, Approximation linearer Ungleichungsrestriktionen im linearen Regressionsmodell, Allgemeines Statistisches Archiv 73 (1989), 184-194. 
  21. [21] P. Stahlecker and G. Trenkler, Linear and ellipsoidal restrictions in linear regression, Statistics 22 (1991), 163-176. Zbl0809.62060
  22. [22] P. Stahlecker and G. Trenkler, Minimax estimation in linear regression with singular covariance structure and convex polyhedral constraints, Journal of Statistical Planning and Inference 36 (1993), 185-196. Zbl0778.62061
  23. [23] S. Tamaschke, Minimax-Schätzer im linearen Regressionsmodell bei nichtkompakten Vorinformationsmengen, Ph. D. thesis, Department of Statistics, University of Dortmund 1997. 
  24. [24] H. Toutenburg, Prior Information in Linear Models, New York: Wiley 1982. 
  25. [25] H.D. Vinod, Bootstrap methods: Applications in econometrics, in H.V. S. Maddala, C.R. Rao (Ed.), Handbook of Statistics, Volume 11 (1993). 
  26. [26] H.J. Werner, On inequality constrained generalized least-squares estimation, Linear Algebra and Its Applications 127 (1990), 379-392. Zbl0701.62066
  27. [27] H.J. Werner and C. Yapar, On inequality constrained generalized least squares selections in the general possibly singular Gauss-Markov model: A projector theoretical approach, Linear Algebra and Its Applications 237/238 (1996), 359-393. Zbl0844.62062

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.