Slow rates of approximation of U-statistics and V-statistics by quadratic forms of Gaussians

Kevin Han Huang, Peter Orbanz

We construct examples of degree-two U- and V-statistics of $n$ i.i.d.~heavy-tailed random vectors in ${\mathbb{R}}^{d(n)}$, whose $\nu$-th moments exist for $\nu >2$, and provide tight…