Empirical process of long-range dependent sequences when parameters are estimated

In this paper, we study the asymptotic behavior of empirical processes when parameters are estimated, assuming that the underlying sequence of random variables is long-range dependent. We show completely different phenomena compared to i.i.d. situation, as well as compared to ordinary empirical processes of long-range dependent sequences. Applications include Kolmogorov–Smirnov and Cramer–Smirnov–von Mises goodness-of-fit statistics.