I was reading the paper "Remarks on some nonparametric estimates of a density function" by Murray Rosenblatt (1956) and in one part he writes that an estimate $S(y;X_1,...,X_n)$ of the density function $f(y)$ of the i.i.d. random variables $X_1,...,X_n$, which is symmetric in the variables $(X_1,...,X_n)$, has as a sufficient statistic the "symmetrised $n$-tuple $(X_1,...,X_n)"$.
Now I was wondering what the "symmetrised" part means exactly?
My best guess is that it means symmetric with respect to permutation, in the sense that for any permutation $\pi\in S_n: (X_1,...,X_n)\stackrel{d}{=}(X_{\pi(1)},...,X_{\pi(n)})$, (where "$\stackrel{d}{=}$" means equal in distribution), but wouldn't that be trivial, as we have i.i.d. random variables?
I tried googling "symmetrised tuple" and I didn't find anything useful. Any help would be very much appreciated. :-)