Shrinkage pre-test estimator of the univariate normal mean

Estimation of the mean of a univariate normal population with unknown variance is a well-known problem in the presence of an uncertain prior information. in this study,we propose a new estimator,shrinkage pre-test estimator,which is a combination of pre-test and shrinkage estimators. the mean squared error (mse) for the shrinkage pre-test estimator is also derived and theoretical comparisons based on mse criterion of this new estimator with the restricted,the pre-test,and the shrinkage estimators are given. we show that the shrinkage pre-test estimator performs better than the other existing estimators. in addition,the performance of this newly proposed estimator is being assessed by conducting a simulation study. © 2010 pakistan journal of statistics.