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Detecting changes in the mean of functional observations

Author

Listed:
  • István Berkes
  • Robertas Gabrys
  • Lajos Horváth
  • Piotr Kokoszka

Abstract

Principal component analysis has become a fundamental tool of functional data analysis. It represents the functional data as "X" "i" ("t")="μ"("t")+Σ 1≤"l">&infin ; "η" "i", "l" + "v" "l" ("t "), where "μ" is the common mean, "v" "l" are the eigenfunctions of the covariance operator and the "η" "i", "l" are the scores. Inferential procedures assume that the mean function "μ"("t") is the same for all values of "i". If, in fact, the observations do not come from one population, but rather their mean changes at some point(s), the results of principal component analysis are confounded by the change(s). It is therefore important to develop a methodology to test the assumption of a common functional mean. We develop such a test using quantities which can be readily computed in the R package fda. The null distribution of the test statistic is asymptotically pivotal with a well-known asymptotic distribution. The asymptotic test has excellent finite sample performance. Its application is illustrated on temperature data from England. Copyright (c) 2009 Royal Statistical Society.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:jorssb:v:71:y:2009:i:5:p:927-946
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Horváth, Lajos & Kokoszka, Piotr & Rice, Gregory, 2014. "Testing stationarity of functional time series," Journal of Econometrics, Elsevier, vol. 179(1), pages 66-82.
    2. repec:bla:jorssb:v:79:y:2017:i:1:p:29-50 is not listed on IDEAS
    3. P. Burdejova & W.K. Härdle & Kokoszka & Q.Xiong, 2015. "Change point and trend analyses of annual expectile curves of tropical storms," SFB 649 Discussion Papers SFB649DP2015-029, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Horváth, Lajos & Hušková, Marie & Rice, Gregory, 2013. "Test of independence for functional data," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 100-119.
    5. Jirak, Moritz, 2012. "Change-point analysis in increasing dimension," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 136-159.
    6. 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, vol. 23(2), pages 256-257, June.
    7. Piotr Kokoszka, 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 276-278, June.
    8. Laha, A. K. & Rathi, Poonam, 2017. "Are the temperature of Indian cities Increasing?: Some Insights Using Change Point Analysis with Functional Data," IIMA Working Papers WP 2017-08-03, Indian Institute of Management Ahmedabad, Research and Publication Department.
    9. Leonid Torgovitski, 2015. "A Darling–Erdős-type CUSUM-procedure for functional data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(1), pages 1-27, January.
    10. 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.
    11. repec:spr:aistmt:v:70:y:2018:i:3:d:10.1007_s10463-017-0606-0 is not listed on IDEAS
    12. Fremdt, Stefan & Horváth, Lajos & Kokoszka, Piotr & Steinebach, Josef G., 2014. "Functional data analysis with increasing number of projections," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 313-332.
    13. Burdejova, P. & Härdle, W. & Kokoszka, P. & Xiong, Q., 2017. "Change point and trend analyses of annual expectile curves of tropical storms," Econometrics and Statistics, Elsevier, vol. 1(C), pages 101-117.
    14. Zhou, Jie, 2011. "Maximum likelihood ratio test for the stability of sequence of Gaussian random processes," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2114-2127, June.

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