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Estimating the number of change points in a sequence of independent normal random variables

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  • Lee, Chung-Bow

Abstract

This work concerns the detection of the number of change points in a sequence of independent normal random variables. An estimator is proposed through some criterion, SC(k), of maximizing the log likelihood function with some penality term. The criterion is similar to that given by Yao (1988) only with a different penality term. An interesting result is that, under mild assumptions, the criterion SC(k) will be monotonically increasing in k [less-than-or-equals, slant] k0 but decreasing in k [greater-or-equal, slanted] k0 with probability approaching 1 as n --> [is proportional to]. Thus, weak consistency of the estimator based on the criterion can easily be obtained.

Suggested Citation

  • Lee, Chung-Bow, 1995. "Estimating the number of change points in a sequence of independent normal random variables," Statistics & Probability Letters, Elsevier, vol. 25(3), pages 241-248, November.
    • Handle: RePEc:eee:stapro:v:25:y:1995:i:3:p:241-248
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    1. Yao, Yi-Ching, 1988. "Estimating the number of change-points via Schwarz' criterion," Statistics & Probability Letters, Elsevier, vol. 6(3), pages 181-189, February.
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    Cited by:

    1. Schroeder, Anna Louise & Fryzlewicz, Piotr, 2013. "Adaptive trend estimation in financial time series via multiscale change-point-induced basis recovery," LSE Research Online Documents on Economics 54934, London School of Economics and Political Science, LSE Library.
    2. Ninomiya, Yoshiyuki, 2005. "Information criterion for Gaussian change-point model," Statistics & Probability Letters, Elsevier, vol. 72(3), pages 237-247, May.
    3. Richard A. Davis & Thomas C. M. Lee & Gabriel A. Rodriguez‐Yam, 2008. "Break Detection for a Class of Nonlinear Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 834-867, September.
    4. Tsai-Hung Fan & Hui-Jane Hsieh & Hsin-Hsian Lee, 2011. "A binary tree algorithm on change points detection," Quality & Quantity: International Journal of Methodology, Springer, vol. 45(3), pages 599-608, April.
    5. Lee, Chung-Bow, 1996. "Nonparametric multiple change-point estimators," Statistics & Probability Letters, Elsevier, vol. 27(4), pages 295-304, May.
    6. Marie Hušková & Zuzana Prášková, 2014. "Comments on: Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 265-269, June.
    7. Kühn, Christoph, 2001. "An estimator of the number of change points based on a weak invariance principle," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 189-196, January.
    8. Fryzlewicz, Piotr, 2020. "Detecting possibly frequent change-points: Wild Binary Segmentation 2 and steepest-drop model selection," LSE Research Online Documents on Economics 103430, London School of Economics and Political Science, LSE Library.

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    Keywords

    Change points Schwarz's criterion;

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