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Mathematical theory of statistics, concerned with formal definitions and general results.

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How to show that a sufficient statistic is NOT minimal sufficient?

As you stated: If there exist $x_1,x_2\in X$ such that $f(x_1)=f(x_2)$ but $g(x_1)\ne g(x_2)$, then $g$ can not be written as a function of $f$, i.e. there exists no function $h$ with $g=h∘f$. So, f …
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