On Shrunken Bayesian Estimators for The Mean of Normal Distribution

Abstract

#This research aims to study the capabilities of two-stage Bayesian shrinkage estimators for estimating the arithmetic mean of the shrinkage coefficient distribution K in the domain R. The research followed an experimental methodology and was divided into an introduction to the topic, three chapters, and a conclusion. The first chapter assumed that χ is a random variable following a normal distribution with an unknown arithmetic mean. The second chapter addressed the case of known variance when prior information about the unknown parameter is available in the form of a prior value. In this case, it is beneficial to use two-stage shrinkage estimators to estimate this parameter. The third chapter discussed the selection of the domain R by minimizing the mean squared error. The conclusion included the main findings, including that the proposed estimator has a lower mean squared error compared to Bayesian estimators, thus resulting in higher relative efficiency.