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Strong convergence rate of estimators of change point and its application

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  • Shi, Xiaoping
  • Wu, Yuehua
  • Miao, Baiqi
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    Abstract

    Let {Xn,n[greater-or-equal, slanted]1} be an independent sequence with a mean shift. We consider the cumulative sum (CUSUM) estimator of a change point. It is shown that, when the rth moment of Xn is finite, for n[greater-or-equal, slanted]1 and r>1, strong convergence rate of the change point estimator is o(M(n)/n), for any M(n) satisfying that M(n)[short up arrow][infinity], which has improved the results in the literature. Furthermore, it is also shown that the preceding rate is still valid for some dependent or negative associate cases. We also propose an iterative algorithm to search for the location of a change point. A simulation study on a mean shift model with a stable distribution is provided, which demonstrates that the algorithm is efficient. In addition, a real data example is given for illustration.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 53 (2009)
    Issue (Month): 4 (February)
    Pages: 990-998

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    Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:990-998

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    Web page: http://www.elsevier.com/locate/csda

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    1. Matula, Przemyslaw, 1992. "A note on the almost sure convergence of sums of negatively dependent random variables," Statistics & Probability Letters, Elsevier, vol. 15(3), pages 209-213, October.
    2. Lavielle, Marc, 1999. "Detection of multiple changes in a sequence of dependent variables," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 79-102, September.
    3. Kokoszka, Piotr & Leipus, Remigijus, 1998. "Change-point in the mean of dependent observations," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 385-393, November.
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    Cited by:
    1. Shi, Xiaoping & Wu, Yuehua & Miao, Baiqi, 2009. "A note on the convergence rate of the kernel density estimator of the mode," Statistics & Probability Letters, Elsevier, vol. 79(17), pages 1866-1871, September.

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