We present two general results that can be used to obtain asymptotic properties for statistical functionals based on linear long-memory sequences. As examples for the first one we consider l- and v-statistics, in particular tail-dependent l-statistics as well as v-statistics with unbounded kernels. As an example for the second result we consider degenerate v-statistics. To prove these results we also establish a weak convergence result for empirical processes of linear long-memory sequences, which improves earlier ones.
Beutner, E. A., Wu, W., & Zähle, H. (2012). Asymptotics for statistical functionals of long-memory sequences. Stochastic Processes and Their Applications, 122(3), 910-929. https://doi.org/10.1016/j.spa.2011.10.006