Asymptotic properties of U-processes under long-range dependence

Céline Lévy-Leduc, Hélène Boistard, Eric Moulines +2

Let $(X_i{)}_{i\ge 1}$ be a stationary mean-zero Gaussian process with covariances $ρ(k)=\PE(X_{1}X_{k+1})$ satisfying: $\rho (0)=1$ and $\rho (k)=k^{-D}L(k)$ where $D$ is in $(0,1)$ and $…