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Asymptotic Behaviour of the Error Probabilities in the Pseudo-Likelihood Ratio Test for Gibbs-Markov Distributions

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Asymptotic Statistics

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

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Abstract

For testing simple statistical hypotheses given by Gibbs-Markov random fields a Bayes test based on the pseudo-likelihood ratio is constructed in order to deal with numerically available quantities. The asymptotic behaviour of the error probabilities is investigated with the aid of an appropriate version of the large deviations theorem. Under natural assumptions the error probabilities are proved to tend to zero exponentially fast.

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References

  • Föllmer, H. and Orey, S. (1988) Large derivations for the empirical field of a Gibbs measure. Ann. Probab. 16 (961–977).

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  • Georgii, H.-D. (1988) Gibbs Measures and Phase Transitions, de Gruyter, Berlin.

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  • Janžura, M. (1984) Discrimination rate of Gibbs random fields for unfitted decision procedure. Proc. 3rd Prague Symp. on Asymp’. Stat. (eds Mandl, P., Hušková, M.). SNTL Praha, 303-308.

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  • Janžura, M. (1987) Large deviations theorem for Gibbs random fields. Proc. of the 5th Pannonian Symp. on Math. Stat. Visegrad 1985 (eds. Grossmann, W., Mogyorodi, J., Vincze, I., Wertz, W.). Akademiai Kiadi, Budapest, 97–112.

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© 1994 Springer-Verlag Berlin Heidelberg

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Janžura, M. (1994). Asymptotic Behaviour of the Error Probabilities in the Pseudo-Likelihood Ratio Test for Gibbs-Markov Distributions. In: Mandl, P., Hušková, M. (eds) Asymptotic Statistics. Contributions to Statistics. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57984-4_23

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  • DOI: https://doi.org/10.1007/978-3-642-57984-4_23

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-0770-7

  • Online ISBN: 978-3-642-57984-4

  • eBook Packages: Springer Book Archive

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