A study on a class of Shrinkage estimators

Primarily parameters of the population are tried to determine in order to make a statistical deduction about any population. Unbiased estimators are widely used for this purpose. It can be mentioned that using biased estimators with smaller mean square error if the unbiased estimator has high mean square error. Accordingly shrinkage estimation methods can be used. Estimators which have smaller mean square error than that of unbiased estimators can be obtained by the help of shrinkage estimation methods. Firstly shrinkage estimation methods are researched and summarized in this study. Then shrinkage estimators for parameters of normal and exponential distribution are analyzed. After that, shrinkage estimators constituted for the shape parameter of Pareto distribution. This biased estimators theoretically compared with unbiased estimators by means of mean square error. Finally, relative efficiencies of biased estimators with regard to unbiased estimators are calculated and conclusions are commented.