Optimal rate of convergence for nonparametric change-point estimators for nonstationary sequences
成果类型：
Article
署名作者：
Ben Hariz, Samir; Wylie, Jonathan J.; Zhang, Qiang
署名单位：
Le Mans Universite; City University of Hong Kong
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/009053606000001596
发表日期：
2007
页码：
1802-1826
关键词：
摘要：
Let (X-i)(i)=1,..., n be a possibly nonstationary sequence such that L(X-i) = P-n, if i <= n theta and 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 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.