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Empirical likelihood ratio test for the change-point problem

Author

Listed:
  • Zou, Changliang
  • Liu, Yukun
  • Qin, Peng
  • Wang, Zhaojun

Abstract

A nonparametric method based on the empirical likelihood is proposed to detect the change-point from a sequence of independent random variables. The empirical likelihood ratio test statistic is proved to have the same limit null distribution as that with classical parametric likelihood. Under some mild conditions, the maximum empirical likelihood estimator of change-point is also shown to be consistent. The simulation results demonstrate the sensitivity and robustness of the proposed approach. A famous real example is studied to illustrate its effectiveness.

Suggested Citation

  • Zou, Changliang & Liu, Yukun & Qin, Peng & Wang, Zhaojun, 2007. "Empirical likelihood ratio test for the change-point problem," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 374-382, February.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:4:p:374-382
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    References listed on IDEAS

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    1. Einmahl, J.H.J. & McKeague, I.W., 2002. "Empirical Likelihood based on Hypothesis Testing," Other publications TiSEM 402576fa-8c0e-45e2-a394-8, Tilburg University, School of Economics and Management.
    2. Gombay, Edit & Horváth, Lajos, 1994. "An application of the maximum likelihood test to the change-point problem," Stochastic Processes and their Applications, Elsevier, vol. 50(1), pages 161-171, March.
    3. Jing, Bing-Yi, 1995. "Two-sample empirical likelihood method," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 315-319, September.
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    5. Yao, Yi-Ching, 1990. "On the asymptotic behavior of a class of nonparametric tests for a change-point problem," Statistics & Probability Letters, Elsevier, vol. 9(2), pages 173-177, February.
    6. Perron, Pierre & Vogelsang, Timothy J, 1992. "Testing for a Unit Root in a Time Series with a Changing Mean: Corrections and Extensions," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(4), pages 467-470, October.
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    Citations

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    Cited by:

    1. Wei Ning, 2012. "Empirical likelihood ratio test for a mean change point model with a linear trend followed by an abrupt change," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 947-961, September.
    2. Shen, Gang, 2013. "On empirical likelihood inference of a change-point," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1662-1668.
    3. Narayanaswamy Balakrishnan & Laurent Bordes & Christian Paroissin & Jean-Christophe Turlot, 2016. "Single change-point detection methods for small lifetime samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(5), pages 531-551, July.
    4. Gabriela Ciuperca & Zahraa Salloum, 2015. "Empirical likelihood test in a posteriori change-point nonlinear model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(8), pages 919-952, November.
    5. Nirian Martín & Leandro Pardo, 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 279-282, June.
    6. Venkata Jandhyala & Stergios Fotopoulos & Ian MacNeill & Pengyu Liu, 2013. "Inference for single and multiple change-points in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 423-446, July.
    7. Cai, Xia & Tian, Yubin & Ning, Wei, 2019. "Change-point analysis of the failure mechanisms based on accelerated life tests," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 515-522.
    8. Mohamed Salah Eddine Arrouch & Echarif Elharfaoui & Joseph Ngatchou-Wandji, 2023. "Change-Point Detection in the Volatility of Conditional Heteroscedastic Autoregressive Nonlinear Models," Mathematics, MDPI, vol. 11(18), pages 1-31, September.
    9. Weizhong Tian & Liyuan Pang & Chengliang Tian & Wei Ning, 2023. "Change Point Analysis for Kumaraswamy Distribution," Mathematics, MDPI, vol. 11(3), pages 1-22, January.
    10. Jean-François Quessy, 2019. "Consistent nonparametric tests for detecting gradual changes in the marginals and the copula of multivariate time series," Statistical Papers, Springer, vol. 60(3), pages 717-746, June.

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