A Comparison of the Pre-test and Shrinkage Estimators for a Finite Population Mean in a Bivariate Normal Distribution with Equal Marginal Variances Under Distrust Coefficient (Journal of Academic Research, 2021)
The estimation of the mean of a bivariate normal population with unknown variance is considered in this paper when uncertain non-sample prior information on the value of the mean and a coefficient of distrust on the null hypothesis is available. Alternative estimators are defined to incorporate both the sample as well as the non-sample information in the estimation process. Some of the important statistical properties of the restricted, preliminary test, and shrinkage estimators are investigated.The performances of the estimators are compared based on the criteria of unbiasedness and mean square error in order to search for a " best” estimator. Both analytical and graphical methods are explored. There is no superior estimator that uniformly dominates the others.In addition, the results showed that neither the preliminary test estimator nor the shrinkage estimator dominates one another except for large dimensions. However, if the non-sample information regarding the value of the mean is close to its true value, the shrinkage estimator over performs the rest of the estimators.