IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v27y2018i4d10.1007_s11749-017-0572-0.html
   My bibliography  Save this article

Strong approximations for the p-fold integrated empirical process with applications to statistical tests

Author

Listed:
  • Sergio Alvarez-Andrade

    (Université de Technologie de Compiègne)

  • Salim Bouzebda

    (Université de Technologie de Compiègne)

  • Aimé Lachal

    (Université de Lyon)

Abstract

The main purpose of this paper is to investigate the strong approximation of the p-fold integrated empirical process, p being a fixed positive integer. More precisely, we obtain the exact rate of the approximations by a sequence of weighted Brownian bridges and a weighted Kiefer process. Our arguments are based in part on the Komlós et al. (Z Wahrscheinlichkeitstheorie und Verw Gebiete 32:111–131, 1975)’s results. Applications include the two-sample testing procedures together with the change-point problems. Finally, simulation results are provided to illustrate the finite sample performance of the proposed statistical tests based on the integrated empirical processes.

Suggested Citation

  • Sergio Alvarez-Andrade & Salim Bouzebda & Aimé Lachal, 2018. "Strong approximations for the p-fold integrated empirical process with applications to statistical tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 826-849, December.
    • Handle: RePEc:spr:testjl:v:27:y:2018:i:4:d:10.1007_s11749-017-0572-0
    DOI: 10.1007/s11749-017-0572-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-017-0572-0
    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/s11749-017-0572-0?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. 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.
    2. Durio, A. & Nikitin, Ya.Yu., 2016. "Local efficiency of integrated goodness-of-fit tests under skew alternatives," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 136-143.
    3. Alexander Aue & Lajos Horváth, 2013. "Structural breaks in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 1-16, January.
    4. Szyszkowicz, Barbara, 1994. "Weak convergence of weighted empirical type processes under contiguous and changepoint alternatives," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 281-313, April.
    5. Lajos Horváth & Gregory Rice, 2014. "Rejoinder 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 287-290, June.
    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. Salim Bouzebda & Youssouf Souddi & Fethi Madani, 2024. "Weak Convergence of the Conditional Set-Indexed Empirical Process for Missing at Random Functional Ergodic Data," Mathematics, MDPI, vol. 12(3), pages 1-22, January.

    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. Stergios B. Fotopoulos & Abhishek Kaul & Vasileios Pavlopoulos & Venkata K. Jandhyala, 2024. "Adaptive parametric change point inference under covariance structure changes," Statistical Papers, Springer, vol. 65(5), pages 2887-2913, July.
    2. Jiang, Feiyu & Wang, Runmin & Shao, Xiaofeng, 2023. "Robust inference for change points in high dimension," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    3. Cho, Haeran & Kirch, Claudia, 2024. "Data segmentation algorithms: Univariate mean change and beyond," Econometrics and Statistics, Elsevier, vol. 30(C), pages 76-95.
    4. Kleiber, Christian, 2016. "Structural Change in (Economic) Time Series," Working papers 2016/06, Faculty of Business and Economics - University of Basel.
    5. Horváth, Lajos & Rice, Gregory & Zhao, Yuqian, 2023. "Testing for changes in linear models using weighted residuals," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    6. Pouliot, William, 2016. "Robust tests for change in intercept and slope in linear regression models with application to manager performance in the mutual fund industry," Economic Modelling, Elsevier, vol. 58(C), pages 523-534.
    7. Marco Barassi & Lajos Horváth & Yuqian Zhao, 2020. "Change‐Point Detection in the Conditional Correlation Structure of Multivariate Volatility Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 340-349, April.
    8. Lajos Horváth & Zhenya Liu & Curtis Miller & Weiqing Tang, 2024. "Breaks in term structures: Evidence from the oil futures markets," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 29(2), pages 2317-2341, April.
    9. Claudia Kirch & Christina Stoehr, 2022. "Sequential change point tests based on U‐statistics," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1184-1214, September.
    10. Bouzebda, Salim & Ferfache, Anouar Abdeldjaoued, 2023. "Asymptotic properties of semiparametric M-estimators with multiple change points," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    11. Horváth, Lajos & Liu, Zhenya & Rice, Gregory & Wang, Shixuan, 2020. "Sequential monitoring for changes from stationarity to mild non-stationarity," Journal of Econometrics, Elsevier, vol. 215(1), pages 209-238.
    12. 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).
    13. Daniela Jarušková, 2015. "Detecting non-simultaneous changes in means of vectors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 681-700, December.
    14. Tianming Xu & Yuesong Wei, 2023. "Ratio Test for Mean Changes in Time Series with Heavy-Tailed AR( p ) Noise Based on Multiple Sampling Methods," Mathematics, MDPI, vol. 11(18), pages 1-14, September.
    15. Zdeněk Hlávka & Marie Hušková & Simos G. Meintanis, 2020. "Change-point methods for multivariate time-series: paired vectorial observations," Statistical Papers, Springer, vol. 61(4), pages 1351-1383, August.
    16. Fabrizio Ghezzi & Eduardo Rossi & Lorenzo Trapani, 2024. "Fast Online Changepoint Detection," Papers 2402.04433, arXiv.org.
    17. Haeran Cho & Claudia Kirch, 2022. "Two-stage data segmentation permitting multiscale change points, heavy tails and dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 653-684, August.
    18. Jaromír Antoch & Jan Hanousek & Lajos Horváth & Marie Hušková & Shixuan Wang, 2019. "Structural breaks in panel data: Large number of panels and short length time series," Econometric Reviews, Taylor & Francis Journals, vol. 38(7), pages 828-855, August.
    19. Lorenzo Escot & Julio E. Sandubete & Łukasz Pietrych, 2023. "Detecting Structural Changes in Time Series by Using the BDS Test Recursively: An Application to COVID-19 Effects on International Stock Markets," Mathematics, MDPI, vol. 11(23), pages 1-18, December.
    20. Yudong Chen & Tengyao Wang & Richard J. Samworth, 2022. "High‐dimensional, multiscale online changepoint detection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(1), pages 234-266, February.

    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:testjl:v:27:y:2018:i:4:d:10.1007_s11749-017-0572-0. 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.