  In this paper we study the asymptotic behaviour 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.
