Improved estimation of regression parameters in measurement error models

The problem of simultaneous estimation of the regression parameters in a multiple regression model with measurement errors is considered when it is suspected that the regression parameter vector may be the null-vector with some degree of uncertainty. In this regard, we propose two sets of four estimators, namely, (i) the unrestricted estimator, (ii) the preliminary test estimator, (iii) the Stein-type estimator and (iv) the postive-rule Stein-type estimator. In an asymptotic setup, properties of these estimators are studied based on asymptotic distributional bias, MSE matrices, and risks under a quadratic loss function. In addition to the asymptotic dominance of the Stein-type estimators, the paper contains discussion of dominating confidence sets based on the Stein-type estimation. Asymptotic analysis is considered based on a sequence of local alternatives to obtain the desired results.