文摘
We propose a nonparametric change point estimator in the distributions of a sequence of independent observations in terms of the test statistics given by Hušková and Meintanis (2006) that are based on weighted empirical characteristic functions. The weight function ω(t; a) under consideration includes the two weight functions from Hušková and Meintanis (2006) plus the weight function used by Matteson and James (2014), where a is a tuning parameter. Under the local alternative hypothesis, we establish the consistency, convergence rate, and asymptotic distribution of this change point estimator which is the maxima of a two-side Brownian motion with a drift. Since the performance of the change point estimator depends on a in use, we thus propose an algorithm for choosing an appropriate value of a, denoted by as which is also justified. Our simulation study shows that the change point estimate obtained by using as has a satisfactory performance. We also apply our method to a real dataset.
