Abstract
In this paper, we have developed a novel approach for deriving shrinkage estimators of means without assuming normality. Our method is based on the equation of the first-order condition with a logarithmic penalty, and it introduces both one-step and two-step shrinkage estimators. The one-step estimator closely resembles the James–Stein estimator, while the differentiable two-step estimator exhibits similar performance to the positive-part Stein estimator. Although the latter does not satisfy Baranchik’s conditions, both estimators can be demonstrated to be minimax under normality assumptions. Furthermore, we have extended this method to handle cases involving an unknown scale. We have successfully applied this approach to the simultaneous estimation of Poisson means.
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