Convergence in distribution of multiple change point estimators |
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Authors: | Maik Döring |
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Institution: | Institute for Applied Mathematics and Statistics, University of Hohenheim, Schloss Hohenheim, 70599 Stuttgart, Germany |
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Abstract: | In this paper we establish the asymptotic distribution for a class of multiple change point estimators in the following setup: a finite sequence of independent random variables consists of segments given by a known number of so-called change points such that the underlying distribution differs from segment to segment. In a nonparametric framework the proposed estimator is defined as the maximizing point of weighted multivariate U-statistic processes. We show that the proposed estimators converge in distribution to a maximizer of a sum of random walks with drift. |
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Keywords: | Change point estimator U-statistic Convergence in distribution |
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