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Change point for multinomial data using phi-divergence test statistics

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  • Apostolos Batsidis

    ()

  • Nirian Martín

    ()

  • Leandro Pardo

    ()

  • Konstantinos Zografos

    ()

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    Abstract

    We propose two families of maximally selected phi-divergence tests for studying change point locations when the unknown probability vectors of a sequence of multinomial random variables, with possibly different sizes, are piecewise constant. In addition, these test-statistics are valid to estimate the location of the change-point. Two variants of the first family are considered by following two versions of the Darling- Erdös' formula. Under the no changes null hypothesis, we derive their limit distributions, extreme value and Gaussian-type respectively. We pay special attention to the checking the accuracy of these limit distributions in case of finite sample sizes. In such a framework, a Monte Carlo analysis shows the possibility of improving the behaviour of the test-statistics based on the likelihood ratio and chi-square tests introduced in Horváth and Serbinowska (1995). The data of the classical Lindisfarne Scribes problem are used in order to apply the proposed test-statistics

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    Bibliographic Info

    Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws110101.

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    Date of creation: Jan 2011
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    Handle: RePEc:cte:wsrepe:ws110101

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    Keywords: Multinomial sampling; Change-point; Phi-divergence test-statistics;

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