Inferential methods for strongly dependent data receive much attention
currently. As the introduction, we argue that this happens not entirely
without reason. The main aim of the lecture is to analyze the behavior
of certain long-range dependent sequences and curve estimators based on
them. We consider a strictly stationary long-range dependent process
(Zi) with standard exponential marginals and the specific bivariate
densities as well as its subordinated process (G(Zi )) for any square
integrable function G. We explain the reasons why the asymptotic
behavior of partial-sum process of a long-range dependent sequence
(G(Zi)) is the same as that of the first non vanishing term of its Laguerre
expansion (Lm(Zi)). Furthermore, convergence in distribution of partial-sum
process to a certain non-Gaussian process is shown. This leads to
it non-central limit theorems for an empirical process and kernel
density estimators.