Discussiones Mathematicae Probability and Statistics 20(1) (2000) 135-161

INFERENCE IN LINEAR MODELS WITH INEQUALITY CONSTRAINED PARAMETERS

Henning Knautz

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

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.

Keywords: inequality constraints, linear regression model, comparison of estimators, Monte Carlo simulation.

1991 Mathematical Subject Classification: Primary: 62J05, Secondary: 62E25.

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Received 10 December 1998
Revised 15 December 1999