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An application of the maximum likelihood test to the change-point problem

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  • Gombay, Edit
  • Horváth, Lajos

Abstract

A maximum-likelihood-type statistic is derived for testing a sequence of observations for no change in the parameter against a possible change. We prove that the limit distribution of the suitably normalized and centralized statistic is double exponential under the null hypothesis.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:50:y:1994:i:1:p:161-171
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    Citations

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    Cited by:

    1. Górecki, Tomasz & Horváth, Lajos & Kokoszka, Piotr, 2018. "Change point detection in heteroscedastic time series," Econometrics and Statistics, Elsevier, vol. 7(C), pages 63-88.
    2. Buddhananda Banerjee & Satyaki Mazumder, 2018. "A more powerful test identifying the change in mean of functional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(3), pages 691-715, June.
    3. 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.
    4. Horvàth, Lajos & Shao, Qi-Man, 1996. "Darling-Erdos-type theorems for sums of Gaussian variables with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 63(1), pages 117-137, October.
    5. Albert Vexler & Chengqing Wu, 2009. "An Optimal Retrospective Change Point Detection Policy," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 542-558, September.
    6. Chioneso S. Marange & Yongsong Qin & Raymond T. Chiruka & Jesca M. Batidzirai, 2023. "A Blockwise Empirical Likelihood Test for Gaussianity in Stationary Autoregressive Processes," Mathematics, MDPI, vol. 11(4), pages 1-20, February.
    7. Gombay, Edit & Serban, Daniel, 2009. "Monitoring parameter change in time series models," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 715-725, April.
    8. Jandhyala, Venkata K. & Fotopoulos, Stergios B. & Hawkins, Douglas M., 2002. "Detection and estimation of abrupt changes in the variability of a process," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 1-19, July.

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