"Derive the asymptotic distribution of Gini's mean difference, which is defined as $$\binom{n}{2}^{-1}\sum\sum_{i<j}|X_i - X_j|."$$
This is a problem from chapter 12 in Van Der Vaart - Asymptotic Statistics. And I feel like I'm not getting any smarter by reading his examples in said chapter since they mostly skip the part of actually deriving the asymptotic distribution and skips directly to the conclusions. ($X_i$ and $X_j$ are i.i.d random variables)
If anybody can explain this to me (alternatively refer me to some other source of information on the subject) that would be great!
Thanks!