Estimate The Mean of Normal Distribution Via Preliminary Test Shrinkage Technique

This paper is concerned with preliminary test single stage shrinkage estimators for the mean (theta) of normal distribution with known variance σ ^2 when a prior estimate (theta 0) of the actule value (theta) is available, using specifying shrinkage weight factor psi(.) as well as pre-test region (R). Expressions for the Bias, Mean Squared Error [MSE(.)] and Relative Efficiency [R.Eff.(.)] of proposed estimators are derived. Numerical results and conclusions are drawn about selection different constants including in these expressions. Comparisons between suggested estimators with respect to usual estimators in the sense of Relative Efficiency are given. Furthermore, comparisons with the earlier existing works are drawn to shown the usefulness of the proposed estimators.