Quadratic form of heavy-tailed self-normalized random vector with applications in $\hat{I}\pm$-heavy Mar\v cenko--Pastur law

Zhaorui Dong, Johannes Heiny, Jianfeng Yao

Let $\mathbf{x}$ be a random vector with $n$ i.i.d.\ real-valued components in the domain attraction of an $\hat{I}\pm$-stable law with $\hat{I}\pm \in (0,2)$, and let $\mathbf{y}=\mathbf{x}/\|\math…