  Let $(X_i)_{i=1,...,n}$ be a possibly nonstationary sequence such that
$\mathscr{L}(X_i)=P_n$ if $i\leq n\theta$ and $\mathscr{L}(X_i)=Q_n$ if
$i>n\theta$, where $0<\theta <1$ is the location of the change-point to be
estimated. We construct a class of estimators based on the empirical measures
and a seminorm on the space of measures defined through a family of functions
$\mathcal{F}$. We prove the consistency of the estimator and give rates of
convergence under very general conditions. In particular, the $1/n$ rate is
achieved for a wide class of processes including long-range dependent sequences
and even nonstationary ones. The approach unifies, generalizes and improves on
the existing results for both parametric and nonparametric change-point
estimation, applied to independent, short-range dependent and as well
long-range dependent sequences.
