ON THOMPSON TYPE ESTIMATORS FOR THE MEAN OF NORMAL DISTRIBUTION
Keywords:normal distribution, shrinkage, preliminary test region, bias ratio, relative efficiency
Let X be a normally distributed with unknown mean μ and variance 2 σ . Assume that a prior estimate 0 μ of μ is available. Two
Thompson type shrinkage estimators of estimating μ that incorporates prior estimate 0 μ are proposed. These estimators are shown to have a smaller mean squared error in a region around 0 μ in comparison to existing estimators. The expressions for the bias and mean squared error of the proposed t-estimators are obtained. Numerical results are provided when the proposed estimators are t-estimators of level of significance α . Comparisons with the earlier known results show the usefulness of the testimators.
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