Minimum mean-squared error estimation in linear regression with an inequality constraint

This paper considers adaptive versions of the minimum mean-squared error estimators in models with an inequality constraint. We derive a sufficient condition under which the proposed class of estimators dominates the traditional inequality constrained least-squares estimator in terms of risk under quadratic loss. Numerical calculations of the risks show that over much of the parameter space, the proposed estimators are superior to the inequality constrained estimator, even if the sufficient condition is not satisfied, and some members of this class have risk advantage over the inequality constrained Stein-rule estimator proposed by Judge et al. (1984, J. Econometrics 25, 165-177) over a wide range of parameter values. © 2000 Elsevier Science B.V.