Optimal rate of convergence for nonparametric change-point estimators for nonstationary sequences

Samir Ben Hariz, Jonathan J. Wylie, Qiang Zhang

Let $(X_i{)}_{i=1,...,n}$ be a possibly nonstationary sequence such that $\mathcal{L}(X_i)=P_n$ if $i\le n\theta$ and $\mathcal{L}(X_i)=Q_n$ if $i>n\theta$, where $0<\theta <1$ is the location of t…