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Detecting and estimating changes in dependent functional data

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  • Aston, John A.D.
  • Kirch, Claudia

Abstract

Change point detection in sequences of functional data is examined where the functional observations are dependent. Of particular interest is the case where the change point is an epidemic change (a change occurs and then the observations return to baseline at a later time). The theoretical properties for various tests for at most one change and epidemic changes are derived with a special focus on power analysis. Estimators of the change point location are derived from the test statistics and theoretical properties are investigated.

Suggested Citation

  • Aston, John A.D. & Kirch, Claudia, 2012. "Detecting and estimating changes in dependent functional data," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 204-220.
  • Handle: RePEc:eee:jmvana:v:109:y:2012:i:c:p:204-220 DOI: 10.1016/j.jmva.2012.03.006
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    References listed on IDEAS

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    1. Aue, Alexander & Gabrys, Robertas & Horváth, Lajos & Kokoszka, Piotr, 2009. "Estimation of a change-point in the mean function of functional data," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2254-2269, November.
    2. István Berkes & Robertas Gabrys & Lajos Horváth & Piotr Kokoszka, 2009. "Detecting changes in the mean of functional observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 927-946.
    3. Jarusková, Daniela & Piterbarg, Vladimir I., 2011. "Log-likelihood ratio test for detecting transient change," Statistics & Probability Letters, Elsevier, pages 552-559.
    4. Peter Hall & Mohammad Hosseini-Nasab, 2006. "On properties of functional principal components analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 109-126.
    5. Horváth, Lajos & Kokoszka, Piotr & Steinebach, Josef, 1999. "Testing for Changes in Multivariate Dependent Observations with an Application to Temperature Changes," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 96-119, January.
    6. Marie Hušková & Claudia Kirch, 2010. "A note on studentized confidence intervals for the change-point," Computational Statistics, Springer, vol. 25(2), pages 269-289, June.
    7. Politis, Dimitris, 2005. "Higher-order accurate, positive semi-definite estimation of large-sample covariance and spectral density matrices," University of California at San Diego, Economics Working Paper Series qt7qg2m9rz, Department of Economics, UC San Diego.
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    Citations

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    Cited by:

    1. John Aston, 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, pages 256-257.
    2. Markevičiūtė, J., 2016. "Epidemic change tests for the mean of innovations of an AR(1) process," Statistics & Probability Letters, Elsevier, pages 79-91.
    3. Bucchia, Béatrice & Wendler, Martin, 2017. "Change-point detection and bootstrap for Hilbert space valued random fields," Journal of Multivariate Analysis, Elsevier, pages 344-368.

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