Synopsis of Project Traditionally the unknown population mean is estimated by the sample mean. Improved estimators, in the sense of admissibility, accuracy and efficiency are recent phenomenon in statistical inference. Improved estimators such as the preliminary test, shrinkage and positive-rule shrinkage estimators, perform better than the traditional estimators based on normal models. When a number of alternative estimators are available to estimate an unknown parameter (scalar or vector) a natural question is, which one should be used and why? The choice obviously depends on the objective of the study and some appropriate criteria to judge the relative performance of the estimators. Generally, in classical theory of statistics, several criteria are employed to judge the characteristics of good estimators. The most common/popular of these criteria include unbiasedness, mean squared error (mse), and quadratic risk. Although the level of emphasis on these criteria varies from application to application, it is desirable that a good estimator will meet the most important/appropriate criterion determined by the researcher, and over perform the rest.