On Weighted Estimation in Linear Regression in th Presence of Parameter Uncertainty

We consider estimating the linear regression model’s coefficients when there is uncertainty about coefficient restrictions. Theorems establish that the mean squared errors of combination estimators, formed as weighted averages of the ordinary least squares and one or more restricted least squares estimators, depend on finding the optimal estimator of a single normally distributed vector. Our results generalize those of Magnus and Durbin (1999) [Magnus, J.R., Durbin, J. 1999. Estimation of regression coefficients of interest when other regression coefficients are of no interest. Econometrica 67, 639-643] and Danilov and Magnus (2004) [Danilov, D., Magnus, J.R. 2004. On the harm that ignoring pretesting can cause. Journal of Econometrics 122, 27-46].