Exact Inference in the Inequality Constrained Normal Linear Regression Model

Inference in the inequality constrained normal linear regression model is approached as a problem in Bayesian inference, using a prior that is the product of a conventional uninformative distribution and an indicator function representing the inequality constraints. The posterior distribution is calculated using Monte Carlo numerical integration, which leads directly to the evaluation of expected values of functions of interest. This approach is compared with others that have been proposed. Three empirical examples illustrate the utility of the proposed methods using an inexpensive 32-bit microcomputer.

[1]  Edward E. Leamer,et al.  Matrix Weighted Averages and Posterior Bounds , 1976 .

[2]  Edward E. Leamer,et al.  A Bayesian Interpretation of Pretesting , 1976 .

[3]  T. Kloek,et al.  Bayesian estimates of equation system parameters, An application of integration by Monte Carlo , 1976 .

[4]  R. Farebrother.  Testing linear inequality constraints in the standard linear model , 1986 .

[5]  W. R. Buckland,et al.  Distributions in Statistics: Continuous Multivariate Distributions , 1973 .

[6]  Anthony O'Hagan,et al.  Bayes estimation of a convex quadratic , 1973 .

[7]  G. Judge,et al.  Inequality Restrictions in Regression Analysis , 1966 .

[8]  Franz C. Palm,et al.  Wald Criteria for Jointly Testing Equality and Inequality , 1986 .

[9]  Edward C. Prescott,et al.  Multiple Regression with Inequality Constraints: Pretesting Bias, Hypothesis Testing and Efficiency , 1970 .

[10]  Anna J. Schwartz,et al.  Monetary Trends in the United States and United Kingdom: Their Relation to Income, Prices, and Interest Rates, 1867–1975 , 1982 .

[11]  R. D. Gordon.  Values of Mills' Ratio of Area to Bounding Ordinate and of the Normal Probability Integral for Large Values of the Argument , 1941 .

[12]  Arnold Zellner,et al.  BAYESIAN ANALYSIS OF THE REGRESSION MODEL WITH AUTOCORRELATED ERRORS. , 1964 .

[13]  C. Gouriéroux,et al.  Likelihood Ratio Test, Wald Test, and Kuhn-Tucker Test in Linear Models with Inequality Constraints on the Regression Parameters , 1982 .

[14]  C. K. Liew,et al.  Inequality Constrained Least-Squares Estimation , 1976 .

[15]  William W. Davis,et al.  Bayesian Analysis of the Linear Model Subject to Linear Inequality Constraints , 1978 .

[16]  G. Judge,et al.  The non-optimality of the inequality restricted estimator under squared error loss , 1984 .