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I have two estimators $T_1$ and $T_2$. $T_1$ is better than $T_2$ based on MSE. But $T_2$ is Pitman closer than $T_1.$ The question is which of these estimators can be useful?

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I have also came acrross this problem before. My advisor stated that "$T_{1}$ is more reasonable than $T_{2}$". see the following paper. https://www.jstor.org/stable/2290692?seq=1#page_scan_tab_contents