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

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Batsidis, Apostolos and Horvath, L. and Martín, N. and Pardo Llorente, Leandro and Zografos, Konstantinos (2013) Change-point detection in multinomial data using phi-divergence test statistics. Journal of multivariate analysis, 118 . pp. 53-66. ISSN 0047-259X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0047259X13000353


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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 Horvath and Serbinowska [7]. The classical Lindisfarne Scribes problem is used to demonstrate the applicability of the proposed statistics to real life data sets.


Item Type:Article
Uncontrolled Keywords:Multinomial sampling; Change-point; Phi-divergence test statistics
Subjects:Sciences > Mathematics > Mathematical statistics
ID Code:22602
Deposited On:29 Jul 2013 08:15
Last Modified:06 Aug 2018 11:10

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