Change point for multinomial data using phi-divergence test statistics

Apostolos Batsidis, Nirian Martín, Leandro Pardo and Konstantinos Zografos

DES - Working Papers. Statistics and Econometrics. WS from Universidad Carlos III de Madrid. Departamento de Estadística

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

Keywords: Multinomial; sampling; Change-point; Phi-divergence; test-statistics (search for similar items in EconPapers)
Date: 2011-01
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