A class of efficient and modified testimators for the mean of normal distribution using complete data

In this paper, we present a class of efficient simulation and modified shrinkage testimators (ST) for the mean µ of normal distribution, when a prior estimate µ<SUB align="right"><SMALL>0</SMALL></SUB> of the mean µ is available from the past. The main idea is to incorporate the prior estimate µ<SUB align="right"><SMALL>0</SMALL></SUB> by modifying the standard shrinkage estimator and considering a feasible form of the shrinkage weight function which is used in both of the estimation steps with different quantities, instead of using a shrinkage weight function in the first step of the shrinkage estimator only. The expressions for the bias, mean squared error, and relative efficiency for both cases when σ<SUP align="right"><SMALL>2</SMALL></SUP> known, or unknown, are derived and studied theoretically and numerically. The resulting testimator dominates the classical estimators in the surprisingly large neighbourhood of the prior estimate µ<SUB align="right"><SMALL>0</SMALL></SUB>. The proposed testimator has been also compared favourably with the existing shrinkage estimators. The discussions regarding the usefulness of these testimators under different situations are provided as conclusions from the various numerical tables obtained from simulation results. Two applications of real data have demonstrated that the method is versatile and not computationally demanding.