Abstract
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 a s which is also justified. Our simulation study shows that the change point estimate obtained by using a s has a satisfactory performance. We also apply our method to a real dataset.
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In memory of Professor Xiru Chen (1934–2005)
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Tan, C., Shi, X., Sun, X. et al. On nonparametric change point estimator based on empirical characteristic functions. Sci. China Math. 59, 2463–2484 (2016). https://doi.org/10.1007/s11425-016-0138-x
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DOI: https://doi.org/10.1007/s11425-016-0138-x
Keywords
- change point estimator
- empirical characteristic function
- tuning parameter
- convergence rate
- asymptotic distribution