I am given continuous i.i.d. random variables $X_1,\dots,X_n$ having an unknown p.d.f. $f$ and am trying to show that the vector of order statistics $(X_{(1)}, \dots, X_{(n)})$ is minimal sufficient for the density function $f$. I have shown sufficiency, but am unsure of how to proceed with the minimality.

I have only seen the definition of minimal sufficiency for parameters, but am assuming that this definition carries over to the case of unknown density functions.


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