科研成果详情

Let (Xi)i=1,...,n be a possibly nonstationary sequence such that script L(Xi) = Pn if i ≤ nθ and script L(Xi) = Qn if i > nθ, where 0 < θ < 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 script 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, shortrange dependent and as well long-range dependent sequences. © Institute of Mathematical Statistics, 2007.