Nonparametric inference in a simple change-point model

In this paper, we consider a change point model allowing at, most one change, X( integral(i/n) + e(i/n), where f(t) = alpha + theta I-(t0,I-1) (l), 0 <= t <= 1, {e(i/n,)....., e(n/n)} is a sequence of i.i.d. random variable, distributed as c with 0 being the median of e. For this change point model, hypothesis test, problem about the change-point t(0) is studied and a test statistic is constructed. Furthermore, a nonparametric estimator of t(0) is proposed and shown to be strongly consistent. Finally, we give an estimator of jump theta and obtain it's asymptotic property. Performance of the proposed approach is investigated by extensive simulation studies.