IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v118y2013icp53-66.html
   My bibliography  Save this article

Change-point detection in multinomial data using phi-divergence test statistics

Author

Listed:
  • Batsidis, A.
  • Horváth, L.
  • Martín, N.
  • Pardo, L.
  • Zografos, K.

Abstract

We propose two families of maximally selected phi-divergence tests to detect a change in the probability vectors of a sequence of multinomial random variables with possibly different sizes. In addition, the proposed statistics can be used to estimate the location of the change-point. We derive the limit distributions of the proposed statistics under the no change null hypothesis. One of the families has an extreme value limit. The limit of the other family is the maximum of the norm of a multivariate Brownian bridge. We check the accuracy of these limit distributions in case of finite sample sizes. A Monte Carlo analysis shows the possibility of improving the behavior of the test statistics based on the likelihood ratio and chi-square tests introduced in Horváth and Serbinowska [7]. The classical Lindisfarne Scribes problem is used to demonstrate the applicability of the proposed statistics to real life data sets.

Suggested Citation

  • Batsidis, A. & Horváth, L. & Martín, N. & Pardo, L. & Zografos, K., 2013. "Change-point detection in multinomial data using phi-divergence test statistics," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 53-66.
    • Handle: RePEc:eee:jmvana:v:118:y:2013:i:c:p:53-66
    DOI: 10.1016/j.jmva.2013.03.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X13000353
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2013.03.008?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. Hawkins, Douglas M., 2001. "Fitting multiple change-point models to data," Computational Statistics & Data Analysis, Elsevier, vol. 37(3), pages 323-341, September.
    2. Gombay, Edit & Horváth, Lajos, 1996. "On the Rate of Approximations for Maximum Likelihood Tests in Change-Point Models," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 120-152, 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. Byungsoo Kim & Junmo Song & Changryong Baek, 2021. "Robust test for structural instability in dynamic factor models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(4), pages 821-853, August.
    2. 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.
    3. Nirian Martín & Leandro Pardo, 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 279-282, 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. Bill Russell & Dooruj Rambaccussing, 2019. "Breaks and the statistical process of inflation: the case of estimating the ‘modern’ long-run Phillips curve," Empirical Economics, Springer, vol. 56(5), pages 1455-1475, May.
    2. Lajos Horvath & Lorenzo Trapani, 2021. "Changepoint detection in random coefficient autoregressive models," Papers 2104.13440, arXiv.org.
    3. Paul Fogel & Yann Gaston-Mathé & Douglas Hawkins & Fajwel Fogel & George Luta & S. Stanley Young, 2016. "Applications of a Novel Clustering Approach Using Non-Negative Matrix Factorization to Environmental Research in Public Health," IJERPH, MDPI, vol. 13(5), pages 1-14, May.
    4. Hans Manner & Bertrand Candelon, 2010. "Testing For Asset Market Linkages: A New Approach Based On Time‐Varying Copulas," Pacific Economic Review, Wiley Blackwell, vol. 15(3), pages 364-384, August.
    5. Salvatore Fasola & Vito M. R. Muggeo & Helmut Küchenhoff, 2018. "A heuristic, iterative algorithm for change-point detection in abrupt change models," Computational Statistics, Springer, vol. 33(2), pages 997-1015, June.
    6. Yann Guédon, 2013. "Exploring the latent segmentation space for the assessment of multiple change-point models," Computational Statistics, Springer, vol. 28(6), pages 2641-2678, December.
    7. Davis, Richard A. & Hancock, Stacey A. & Yao, Yi-Ching, 2016. "On consistency of minimum description length model selection for piecewise autoregressions," Journal of Econometrics, Elsevier, vol. 194(2), pages 360-368.
    8. Antoch, Jaromír & Husková, Marie, 2001. "Permutation tests in change point analysis," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 37-46, May.
    9. 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.
    10. Kang-Ping Lu & Shao-Tung Chang, 2021. "Robust Algorithms for Change-Point Regressions Using the t -Distribution," Mathematics, MDPI, vol. 9(19), pages 1-28, September.
    11. Venkata Jandhyala & Stergios Fotopoulos & Ian MacNeill & Pengyu Liu, 2013. "Inference for single and multiple change-points in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 423-446, July.
    12. Aki-Hiro Sato & Hideki Takayasu, 2013. "Segmentation procedure based on Fisher's exact test and its application to foreign exchange rates," Papers 1309.0602, arXiv.org.
    13. Michele Rienzner & Francesca Ieva, 2017. "Critical values improvement for the standard normal homogeneity test by combining Monte Carlo and regression approaches," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(4), pages 602-619, March.
    14. Sandip Sinharay, 2017. "Some Remarks on Applications of Tests for Detecting A Change Point to Psychometric Problems," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1149-1161, December.
    15. Kang-Ping Lu & Shao-Tung Chang, 2023. "An Advanced Segmentation Approach to Piecewise Regression Models," Mathematics, MDPI, vol. 11(24), pages 1-23, December.
    16. Galeano, Pedro, 2007. "The use of cumulative sums for detection of changepoints in the rate parameter of a Poisson Process," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6151-6165, August.
    17. Jaromír Antoch & Daniela Jarušková, 2013. "Testing for multiple change points," Computational Statistics, Springer, vol. 28(5), pages 2161-2183, October.
    18. Aurelio Fernández Bariviera & M. Belén Guercio & Lisana B. Martinez, 2014. "Informational Efficiency in Distressed Markets: The Case of European Corporate Bonds," The Economic and Social Review, Economic and Social Studies, vol. 45(3), pages 349-369.
    19. Stergios B. Fotopoulos & Alex Paparas & Venkata K. Jandhyala, 2022. "Change point detection and estimation methods under gamma series of observations," Statistical Papers, Springer, vol. 63(3), pages 723-754, June.
    20. Bill Russell & Dooruj Rambaccussing, 2016. "Breaks and the Statistical Process of Inflation: The Case of the ‘Modern’ Phillips Curve," Dundee Discussion Papers in Economics 294, Economic Studies, University of Dundee.

    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:118:y:2013:i:c:p:53-66. 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.