IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v61y2020i4d10.1007_s00362-020-01161-9.html
   My bibliography  Save this article

Convergence of U-processes in Hölder spaces with application to robust detection of a changed segment

Author

Listed:
  • Alfredas Račkauskas

    (Vilnius University)

  • Martin Wendler

    (Otto von Guericke Universität Magdeburg)

Abstract

To detect a changed segment (so called epidemic changes) in a time series, variants of the CUSUM statistic are frequently used. However, they are sensitive to outliers in the data and do not perform well for heavy tailed data, especially when short segments get a high weight in the test statistic. We will present a robust test statistic for epidemic changes based on the Wilcoxon statistic. To study their asymptotic behavior, we prove functional limit theorems for U-processes in Hölder spaces. We also study the finite sample behavior via simulations and apply the statistic to a real data example.

Suggested Citation

  • Alfredas Račkauskas & Martin Wendler, 2020. "Convergence of U-processes in Hölder spaces with application to robust detection of a changed segment," Statistical Papers, Springer, vol. 61(4), pages 1409-1435, August.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:4:d:10.1007_s00362-020-01161-9
    DOI: 10.1007/s00362-020-01161-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-020-01161-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-020-01161-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Gombay, Edit, 2001. "U-Statistics for Change under Alternatives," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 139-158, July.
    2. A. N. Pettitt, 1979. "A Non‐Parametric Approach to the Change‐Point Problem," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 28(2), pages 126-135, June.
    3. Kabluchko, Zakhar & Wang, Yizao, 2014. "Limiting distribution for the maximal standardized increment of a random walk," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2824-2867.
    4. Annika Betken, 2016. "Testing for Change-Points in Long-Range Dependent Time Series by Means of a Self-Normalized Wilcoxon Test," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(6), pages 785-809, November.
    5. Shao, Xiaofeng & Zhang, Xianyang, 2010. "Testing for Change Points in Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1228-1240.
    6. Herold Dehling & Aeneas Rooch & Murad S. Taqqu, 2013. "Non-Parametric Change-Point Tests for Long-Range Dependent Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(1), pages 153-173, March.
    7. Dietmar Ferger, 1994. "On the power of nonparametric changepoint-tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 41(1), pages 277-292, December.
    8. Gombay, Edit, 1994. "Testing for change-points with rank and sign statistics," Statistics & Probability Letters, Elsevier, vol. 20(1), pages 49-55, May.
    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. Georgy Sofronov & Martin Wendler & Volkmar Liebscher, 2020. "Editorial for the special issue: Change point detection," Statistical Papers, Springer, vol. 61(4), pages 1347-1349, August.
    2. Joseph Ngatchou-Wandji & Echarif Elharfaoui & Michel Harel, 2022. "On change-points tests based on two-samples U-Statistics for weakly dependent observations," Statistical Papers, Springer, vol. 63(1), pages 287-316, February.

    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. Kai Wenger & Christian Leschinski & Philipp Sibbertsen, 2019. "Change-in-mean tests in long-memory time series: a review of recent developments," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(2), pages 237-256, June.
    2. Lazar, Emese & Wang, Shixuan & Xue, Xiaohan, 2023. "Loss function-based change point detection in risk measures," European Journal of Operational Research, Elsevier, vol. 310(1), pages 415-431.
    3. Wenger, Kai & Leschinski, Christian & Sibbertsen, Philipp, 2018. "A simple test on structural change in long-memory time series," Economics Letters, Elsevier, vol. 163(C), pages 90-94.
    4. Lajos Horváth & Gregory Rice, 2014. "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 219-255, June.
    5. Joseph Ngatchou-Wandji & Echarif Elharfaoui & Michel Harel, 2022. "On change-points tests based on two-samples U-Statistics for weakly dependent observations," Statistical Papers, Springer, vol. 63(1), pages 287-316, February.
    6. Junwei Hu & Lihong Wang, 2023. "A weighted U-statistic based change point test for multivariate time series," Statistical Papers, Springer, vol. 64(3), pages 753-778, June.
    7. Matúš Maciak & Michal Pešta & Barbora Peštová, 2020. "Changepoint in dependent and non-stationary panels," Statistical Papers, Springer, vol. 61(4), pages 1385-1407, August.
    8. Wingert, Simon & Mboya, Mwasi Paza & Sibbertsen, Philipp, 2020. "Distinguishing between breaks in the mean and breaks in persistence under long memory," Economics Letters, Elsevier, vol. 193(C).
    9. Dooruj Rambaccussing & Murat Mazibas, 2020. "True versus Spurious Long Memory in Cryptocurrencies," JRFM, MDPI, vol. 13(9), pages 1-11, August.
    10. Michal Pešta & Martin Wendler, 2020. "Nuisance-parameter-free changepoint detection in non-stationary series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 379-408, June.
    11. Tabacu, Lucia & Ledbetter, Mark, 2019. "Change-point analysis using logarithmic quantile estimation," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 94-100.
    12. Liu, Bin & Zhou, Cheng & Zhang, Xinsheng, 2019. "A tail adaptive approach for change point detection," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 33-48.
    13. Wenger, Kai & Leschinski, Christian, 2021. "Fixed-bandwidth CUSUM tests under long memory," Econometrics and Statistics, Elsevier, vol. 20(C), pages 46-61.
    14. Choi, Ji-Eun & Shin, Dong Wan, 2020. "A self-normalization test for correlation change," Economics Letters, Elsevier, vol. 193(C).
    15. Wenger, Kai & Less, Vivien, 2020. "A modified Wilcoxon test for change points in long-range dependent time series," Economics Letters, Elsevier, vol. 192(C).
    16. Hoga, Yannick, 2017. "Monitoring multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 105-121.
    17. Stephen J. Déry & Marco A. Hernández-Henríquez & Tricia A. Stadnyk & Tara J. Troy, 2021. "Vanishing weekly hydropeaking cycles in American and Canadian rivers," Nature Communications, Nature, vol. 12(1), pages 1-12, December.
    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. Kazi Ali Tamaddun & Ajay Kalra & Sajjad Ahmad, 2019. "Spatiotemporal Variation in the Continental US Streamflow in Association with Large-Scale Climate Signals Across Multiple Spectral Bands," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(6), pages 1947-1968, April.
    20. Jie Yang & Yimin Wang & Jun Yao & Jianxia Chang & Guoxin Xu & Xin Wang & Hui Hu, 2020. "Coincidence probability analysis of hydrologic low-flow under the changing environment in the Wei River Basin," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 103(2), pages 1711-1726, September.

    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:spr:stpapr:v:61:y:2020:i:4:d:10.1007_s00362-020-01161-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.