## Stein-like Estimator

We consider an empirical Bayes approach to a Stein's estimator by Efron and Morris, and use it as a guideline to construct a ``Stein-like'' estimator for . Here we fix the adverse event to obtain the estimate simultaneously for all . We assume that approximately are independent for all , and that . Then we can define the estimator of by

where . Here we use the estimate

Furthermore, the estimate will be obtained as the MLE of on the basis of ; thus, it becomes the solution to

with . Together we can obtain the stein-like estimator of relative reprot rate by

where we use .

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