Some improved two-stage shrinkage testimators for the mean of normal distribution

Abstract

In this paper, we introduced some two-stage shrinkage testimators (TSST) for the mean μ when a prior estimate μ0 of the mean μ is available from the past, by considering a feasible form of the shrinkage weight function which is used in both of the estimation stages with different quantities. The expressions for the bias, mean squared error, expected sample size and relative efficiency for the both cases when 2 known or unknown, are derived and studied. The discussion regarding the usefulness of these testimators under different situations is provided as conclusions from various numerical tables obtained from simulation results.