The problem of shrinking the maximum likelihood estimator (MLE) of the mean μ of various populations towards a natural origin μ0 is studied. Estimators of the general form, are proposed for the cases of Normal, Gamma, Poisson, and Binomial distributions. The behavior of these estimators is compared with that of the ones suggested by Thompson [3]. Our estimators are shown to be better in the sense of having a smaller mean square error in an interval around μ0.
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Mehta et al. (1971) studied this question.
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