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Empirical likelihood ratio test for a mean change point model with a linear trend followed by an abrupt change

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  • Wei Ning

Abstract

In this paper, a change point model with the mean being constant up to some unknown point, and increasing linearly to another unknown point, then dropping back to the original level is studied. A nonparametric method based on the empirical likelihood test is proposed to detect and estimate the locations of change points. Under some mild conditions, the asymptotic null distribution of an empirical likelihood ratio test statistic is shown to have the extreme distribution. The consistency of the test is also proved. Simulations of the powers of the test indicate that it performs well under different assumptions of the data distribution. The test is applied to the aircraft arrival time data set and the Stanford heart transplant data set.

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  • 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.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:5:p:947-961
    DOI: 10.1080/02664763.2011.628647
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    1. 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.
    2. Zhong Guan, 2004. "A semiparametric changepoint model," Biometrika, Biometrika Trust, vol. 91(4), pages 849-862, December.
    3. Ashish Sen & S. Srivastava, 1975. "On tests for detecting change in mean when variance is unknown," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 27(1), pages 479-486, December.
    4. Chen, Yu-Wang & Lu, Yong-Zai & Chen, Peng, 2007. "Optimization with extremal dynamics for the traveling salesman problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(1), pages 115-123.
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    Cited by:

    1. 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.

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