IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v100y2009i10p2254-2269.html
   My bibliography  Save this article

Estimation of a change-point in the mean function of functional data

Author

Listed:
  • Aue, Alexander
  • Gabrys, Robertas
  • Horváth, Lajos
  • Kokoszka, Piotr

Abstract

The paper develops a comprehensive asymptotic theory for the estimation of a change-point in the mean function of functional observations. We consider both the case of a constant change size, and the case of a change whose size approaches zero, as the sample size tends to infinity. We show how the limit distribution of a suitably defined change-point estimator depends on the size and location of the change. The theoretical insights are confirmed by a simulation study which illustrates the behavior of the estimator in finite samples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:10:p:2254-2269
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(09)00082-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Garcia, Rene & Ghysels, Eric, 1998. "Structural change and asset pricing in emerging markets," Journal of International Money and Finance, Elsevier, vol. 17(3), pages 455-473, June.
    2. Antoniadis, Anestis & Sapatinas, Theofanis, 2007. "Estimation and inference in functional mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4793-4813, June.
    3. Laukaitis, Algirdas & Rackauskas, Alfredas, 2005. "Functional data analysis for clients segmentation tasks," European Journal of Operational Research, Elsevier, vol. 163(1), pages 210-216, May.
    4. Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
    5. Antoniadis, Anestis & Sapatinas, Theofanis, 2003. "Wavelet methods for continuous-time prediction using Hilbert-valued autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 133-158, October.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Axel Bücher & Holger Dette & Florian Heinrichs, 2020. "Detecting deviations from second-order stationarity in locally stationary functional time series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 1055-1094, August.
    2. Aneiros, Germán & Horová, Ivana & Hušková, Marie & Vieu, Philippe, 2022. "On functional data analysis and related topics," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Castrillón-Candás, Julio E. & Kon, Mark, 2022. "Anomaly detection: A functional analysis perspective," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    4. Horváth, Lajos & Rice, Gregory & Zhao, Yuqian, 2022. "Change point analysis of covariance functions: A weighted cumulative sum approach," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    5. Han Lin Shang & Jiguo Cao & Peijun Sang, 2022. "Stopping time detection of wood panel compression: A functional time‐series approach," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1205-1224, November.
    6. B. Cooper Boniece & Lajos Horv'ath & Lorenzo Trapani, 2023. "On changepoint detection in functional data using empirical energy distance," Papers 2310.04853, arXiv.org.
    7. Trevor Harris & Bo Li & J. Derek Tucker, 2022. "Scalable multiple changepoint detection for functional data sequences," Environmetrics, John Wiley & Sons, Ltd., vol. 33(2), March.
    8. Jirak, Moritz, 2012. "Change-point analysis in increasing dimension," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 136-159.
    9. Dennis Schroers, 2024. "Robust Functional Data Analysis for Stochastic Evolution Equations in Infinite Dimensions," Papers 2401.16286, arXiv.org.
    10. Mengchen Wang & Trevor Harris & Bo Li, 2023. "Asynchronous Changepoint Estimation for Spatially Correlated Functional Time Series," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(1), pages 157-176, March.
    11. Xu, Haotian & Wang, Daren & Zhao, Zifeng & Yu, Yi, 2022. "Change point inference in high-dimensional regression models under temporal dependence," LIDAM Discussion Papers ISBA 2022027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Veronika Římalová & Alessandra Menafoglio & Alessia Pini & Vilém Pechanec & Eva Fišerová, 2020. "A permutation approach to the analysis of spatiotemporal geochemical data in the presence of heteroscedasticity," Environmetrics, John Wiley & Sons, Ltd., vol. 31(4), June.
    13. Stoehr, Christina & Aston, John A D & Kirch, Claudia, 2021. "Detecting changes in the covariance structure of functional time series with application to fMRI data," Econometrics and Statistics, Elsevier, vol. 18(C), pages 44-62.
    14. Kraus, David, 2019. "Inferential procedures for partially observed functional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 583-603.
    15. van Delft, Anne & Eichler, Michael, 2017. "Locally Stationary Functional Time Series," LIDAM Discussion Papers ISBA 2017023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    16. Jialiang Li & Yaguang Li & Tailen Hsing, 2022. "On functional processes with multiple discontinuities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 933-972, July.
    17. 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.
    18. Woody, Jonathan, 2015. "Time series regression with persistent level shifts," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 22-29.
    19. Tadas Danielius & Alfredas Račkauskas, 2022. "Multiple Change-Point Detection in a Functional Sample via the 𝒢-Sum Process," Mathematics, MDPI, vol. 10(13), pages 1-27, June.
    20. J. Derek Tucker & Drew Yarger, 2024. "Elastic functional changepoint detection of climate impacts from localized sources," Environmetrics, John Wiley & Sons, Ltd., vol. 35(1), February.
    21. Rice, Gregory & Zhang, Chi, 2022. "Consistency of binary segmentation for multiple change-point estimation with functional data," Statistics & Probability Letters, Elsevier, vol. 180(C).
    22. 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.
    23. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lajos Horváth & Gregory Rice, 2015. "Testing Equality Of Means When The Observations Are From Functional Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(1), pages 84-108, January.
    2. Elena Andreou & Eric Ghysels, 2002. "Tests for Breaks in the Conditional Co-movements of Asset Returns," CIRANO Working Papers 2002s-59, CIRANO.
    3. Shang, Han Lin & Hyndman, Rob.J., 2011. "Nonparametric time series forecasting with dynamic updating," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1310-1324.
    4. 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.
    5. Horváth, Lajos & Husková, Marie & Kokoszka, Piotr, 2010. "Testing the stability of the functional autoregressive process," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 352-367, February.
    6. 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, November.
    7. van Delft, Anne & Eichler, Michael, 2017. "Locally Stationary Functional Time Series," LIDAM Discussion Papers ISBA 2017023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Ana-Maria Staicu & Yingxing Li & Ciprian M. Crainiceanu & David Ruppert, 2014. "Likelihood Ratio Tests for Dependent Data with Applications to Longitudinal and Functional Data Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 932-949, December.
    9. Hoga, Yannick, 2017. "Monitoring multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 105-121.
    10. Mingotti, Nicola & Lillo Rodríguez, Rosa Elvira & Romo, Juan, 2015. "A Random Walk Test for Functional Time Series," DES - Working Papers. Statistics and Econometrics. WS ws1506, Universidad Carlos III de Madrid. Departamento de Estadística.
    11. Garcia, Rene & Bonomo, Marco, 2001. "Tests of conditional asset pricing models in the Brazilian stock market," Journal of International Money and Finance, Elsevier, vol. 20(1), pages 71-90, February.
    12. Barr, David G. & Priestley, Richard, 2004. "Expected returns, risk and the integration of international bond markets," Journal of International Money and Finance, Elsevier, vol. 23(1), pages 71-97, February.
    13. Zhang, Xianyang, 2016. "White noise testing and model diagnostic checking for functional time series," Journal of Econometrics, Elsevier, vol. 194(1), pages 76-95.
    14. Rady, E.A. & Kilany, N.M. & Eliwa, S.A., 2015. "Estimation in mixed-effects functional ANOVA models," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 346-355.
    15. María Edo & Walter Sosa Escudero & Marcela Svarc, 2021. "A multidimensional approach to measuring the middle class," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 19(1), pages 139-162, March.
    16. Jarry, Gabriel & Delahaye, Daniel & Nicol, Florence & Feron, Eric, 2020. "Aircraft atypical approach detection using functional principal component analysis," Journal of Air Transport Management, Elsevier, vol. 84(C).
    17. Guangxing Wang & Sisheng Liu & Fang Han & Chong‐Zhi Di, 2023. "Robust functional principal component analysis via a functional pairwise spatial sign operator," Biometrics, The International Biometric Society, vol. 79(2), pages 1239-1253, June.
    18. 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.
    19. Michal Benko & Wolfgang Härdle & Alois Kneip, 2006. "Common Functional Principal Components," SFB 649 Discussion Papers SFB649DP2006-010, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    20. Goriaev, Alexei & Zabotkin, Alexei, 2006. "Risks of investing in the Russian stock market: Lessons of the first decade," Emerging Markets Review, Elsevier, vol. 7(4), pages 380-397, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:100:y:2009:i:10:p:2254-2269. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.