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.
- Degenerate V-statistic
- Linear long-memory sequence
- Modified Functional Delta Method
- Noncentral limit theorem
- Quasi-Hadamard differentiability
- U- and V-statistics
- Weighted empirical process