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

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  • 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
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    References listed on IDEAS

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    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.
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    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. 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.
    3. 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.

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