In this paper, we consider a change point model allowing at most one change, X($\tfrac{i}{n}$\tfrac{i}{n}) = f($\tfrac{i}{n}$\tfrac{i}{n}) + e($\tfrac{i}{n}$\tfrac{i}{n}), where f(t) = α + θ $I_{(t_0 ,1)} $I_{(t_0 ,...In this paper, we consider a change point model allowing at most one change, X($\tfrac{i}{n}$\tfrac{i}{n}) = f($\tfrac{i}{n}$\tfrac{i}{n}) + e($\tfrac{i}{n}$\tfrac{i}{n}), where f(t) = α + θ $I_{(t_0 ,1)} $I_{(t_0 ,1)} (t), 0 ≤ t ≤ 1, {e($\tfrac{1}{n}$\tfrac{1}{n}), ..., e($\tfrac{n}{n}$\tfrac{n}{n})} is a sequence of i.i.d. random variables distributed as e with 0 being the median of e. For this change point model, hypothesis test problem about the change-point t0 is studied and a test statistic is constructed. Furthermore, a nonparametric estimator of t0 is proposed and shown to be strongly consistent. Finally, we give an estimator of jump θ and obtain it’s asymptotic property. Performance of the proposed approach is investigated by extensive simulation studies.展开更多
基金National Natural Science Foundation of China (Grant No.10471136)Ph.D.Program Foundation of the Ministry of Education of ChinaSpecial Foundations of the Chinese Academy of Sciences and USTC
文摘In this paper, we consider a change point model allowing at most one change, X($\tfrac{i}{n}$\tfrac{i}{n}) = f($\tfrac{i}{n}$\tfrac{i}{n}) + e($\tfrac{i}{n}$\tfrac{i}{n}), where f(t) = α + θ $I_{(t_0 ,1)} $I_{(t_0 ,1)} (t), 0 ≤ t ≤ 1, {e($\tfrac{1}{n}$\tfrac{1}{n}), ..., e($\tfrac{n}{n}$\tfrac{n}{n})} is a sequence of i.i.d. random variables distributed as e with 0 being the median of e. For this change point model, hypothesis test problem about the change-point t0 is studied and a test statistic is constructed. Furthermore, a nonparametric estimator of t0 is proposed and shown to be strongly consistent. Finally, we give an estimator of jump θ and obtain it’s asymptotic property. Performance of the proposed approach is investigated by extensive simulation studies.
