An alternative representation of the Wilcoxon signed rank statistic $V$ is
$V=\sum_{i\le j}\mathbb{I}_{\{X_i+X_j>0\}}=\sum_i\mathbb{I}_{\{X_i>0\}}+\sum_{i<j}\mathbb{I}_{\{X_i+X_j>0\}}$
where $X_1,\cdots, X_n$ are i.i.d. .
How to find the limiting distribution of $V$ without requiring that $X_i$ has a symmetric distribution?
I know it can be solved by projection method. But I don't know exactly how it works. Who can help me write down the details of the proof?
Thanks a lot.