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Abstract:
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We consider the problem of estimating multiple change points for a functional data process. There are many scientific and business examples where the underlying process may undergo some sudden changes in the mean. The process data that are not in a close vicinity of any change point can be analyzed by the usual nonparametric smoothing methods. However, the data observed close to a change point contain the most pertinent information of the structural break and need to be handled differently. This paper considers a half-kernel approach that addresses the inference of the total number, locations, and jump sizes of the changes. Asymptotic properties including convergence rates of the proposed procedures are thoroughly investigated. Simulations are conducted to examine the performance of the approach, and a number of real data sets are analyzed to provide an illustration.
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