Inference in linear models with inequality constrained parameters

• Autorzy: Henning Knautz
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

inequality constraints; linear regression model; comparison of estimators; Monte Carlo simulation

Kategorie tematyczne

• 62J05: Linear regression

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2000
• Tom: 20
• Numer: 1
• Strony: 135-161

Daty

wydano

2000

otrzymano

1998-12-10

poprawiono

1999-12-15

Twórcy

autor

Henning Knautz

• Institute for Statistics and Econometrics, University of Hamburg, Von-Melle-Park 5, D-20146 Hamburg

Bibliografia

• [1] G. Box and G. Tiao, Bayesian Inference in Statistical Analysis, New York: Wiley (1973), reprinted in: Wiley Classics Library Edition 1992.
• [2] W. Davis, Bayesian analysis of the linear model subject to linear inequality constraints, JASA 73 (363) (1978), 573-579.
• [3] J. Geweke, Exact inference in the inequality constrained normal linear regression model, Journal of Applied Econometrics 1 (1986), 127-141.
• [4] J. Geweke, Bayesian inference in econometric models using Monte Carlo integration, Econometrica 57 (6) (1989), 1317-1339.
• [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.
• [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] C. Gourieroux and A. Monfort, Statistics and Econometric Models, Volume 1+2 Cambridge University Press (1995).
• [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] J. Judge and T. Takayama, Inequality restrictions in regression analysis, Journal of the American Statistical Association 61 (1966), 166-181.
• [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.
• [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.
• [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.
• [13] C.Liew, Inequality constrained least squares estimation, Journal of the American Statistical Association 71 (1976), 746-751.
• [14] D.G. Luenberger, Linear and Nonlinear Programming, (2nd ed.) Addison Wesley 1984.
• [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.
• [16] J. Pilz, Bayesian Estimation and Experimental Design in Linear Regression Models, New York: Wiley 1991.
• [17] R. Pindyck and D. Rubinfeld, Econometric Models and Forecasts, New York: Wiley.
• [18] R. Schoenberg, Constrained maximum likelihood, Computational Economics 10 (1997), 251-266.
• [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.
• [20] P. Stahlecker and K. Schmidt, Approximation linearer Ungleichungsrestriktionen im linearen Regressionsmodell, Allgemeines Statistisches Archiv 73 (1989), 184-194.
• [21] P. Stahlecker and G. Trenkler, Linear and ellipsoidal restrictions in linear regression, Statistics 22 (1991), 163-176.
• [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.
• [23] S. Tamaschke, Minimax-Schätzer im linearen Regressionsmodell bei nichtkompakten Vorinformationsmengen, Ph. D. thesis, Department of Statistics, University of Dortmund 1997.
• [24] H. Toutenburg, Prior Information in Linear Models, New York: Wiley 1982.
• [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] H.J. Werner, On inequality constrained generalized least-squares estimation, Linear Algebra and Its Applications 127 (1990), 379-392.
• [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.

Identyfikatory

DOI

10.7151/dmps.1008