Given $X_1, X_2,\ldots, X_n$ are i.i.d with $f(x) = \frac{1}{\pi}\frac{1}{1+x^2}$. Find the minimal sufficient statistic for $\frac{1}{\pi^{n}(\prod_{i=1}^{n} 1+(x_i-\theta)^2)}$.
My question: Using Bahadur's Factorization and Lehman-Scheffe's theorems, I obtain the sufficient statistic as $T(X) = (x_1, \ldots, x_n)$. However, the correct answer turned out to be $T(X) = (x_{(1)}, x_{(2)},\ldots, x_{(n)})$. But I cannot see why the first answer is incorrect, because if we are given the entire sample set, we could easily obtain the order statistic of that sample, so how could $T(X) = (x_1, \ldots, x_n)$ is wrong?