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A procedure for lowering the mean square error (MSE) of the minimum variance unbiased linear estimator (MVULE) of the mean of a population is considered. The technique employed is shrinkage of the MVULE towards a natural origin, μ0, in the parameter space. The suggested estimator is: The case where μ0 = 0 is given special consideration. This is the general case for the normal distribution. When |μ/σz| is small, shrinkage buys decreased MSE at the expense of increased MSE for |μ/σz| large.
James R. Thompson (Fri,) studied this question.