If $X_{(1)}, X_{(2)},\ldots$ are mutually dependent as in the case of ordered statistics and we need to find the sum $S_N$ of all $X_{(i)}$ like $\sum_{i=1}^{N\to \infty} X_{(i)}$.
How do we apply the CLT in this case?
I've been searching around but all I could find is the CLT for sum of I.I.D. random variables. I haven't found anything for cases when the R.V.s are Non-I.I.D.
I hope my question is clear enough. If not, please be gentle.