Improved Estimation in Measurement Error Models Through Stein Rule Procedure

This paper examines the role of Stein estimation in a linear ultrastructural form of the measurement errors model. It is demonstrated that the application of Stein rule estimation to the matrix of true values of regressors leads to the overcoming of the inconsistency of the least squares procedure and yields consistent estimators of regression coefficients. A further application may improve the efficiency properties of the estimators of regression coefficients. It is observed that the proposed family of estimators under some constraint on the characterizing scalar dominates the conventional consistent estimator with respect to the criterion of asymptotic risk under a specific quadratic loss function. Then the problem of prediction of the values of the study variable within the sample is considered, and it is found that the predictors based on the proposed family of estimators are always more efficient than the predictors based on the conventional estimator according to asymptotic predictive mean squared error criterion, although both are biased.