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Detecting changes in the mean of functional observations


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


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.

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Bibliographic Info

Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).

Volume (Year): 71 (2009)
Issue (Month): 5 ()
Pages: 927-946

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Handle: RePEc:bla:jorssb:v:71:y:2009:i:5:p:927-946

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Cited by:
  1. Zhou, Jie, 2011. "Maximum likelihood ratio test for the stability of sequence of Gaussian random processes," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 55(6), pages 2114-2127, June.
  2. 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, Springer, vol. 23(2), pages 276-278, June.
  3. 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, Springer, vol. 23(2), pages 256-257, June.
  4. Horváth, Lajos & Hušková, Marie & Rice, Gregory, 2013. "Test of independence for functional data," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 117(C), pages 100-119.
  5. Fremdt, Stefan & Horváth, Lajos & Kokoszka, Piotr & Steinebach, Josef G., 2014. "Functional data analysis with increasing number of projections," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 124(C), pages 313-332.
  6. Horváth, Lajos & Kokoszka, Piotr & Rice, Gregory, 2014. "Testing stationarity of functional time series," Journal of Econometrics, Elsevier, Elsevier, vol. 179(1), pages 66-82.


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