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On divergence tests for composite hypotheses under composite likelihood

Author

Listed:
  • N. Martín

    (Complutense University of Madrid)

  • L. Pardo

    (Complutense University of Madrid)

  • K. Zografos

    (University of Ioannina)

Abstract

It is well-known that in some situations it is not easy to compute the likelihood function as the datasets might be large or the model is too complex. In that contexts composite likelihood, derived by multiplying the likelihoods of subjects of the variables, may be useful. The extension of the classical likelihood ratio test statistics to the framework of composite likelihoods is used as a procedure to solve the problem of testing in the context of composite likelihood. In this paper we introduce and study a new family of test statistics for composite likelihood: Composite $$\phi $$ ϕ -divergence test statistics for solving the problem of testing a simple null hypothesis or a composite null hypothesis. To do that we introduce and study the asymptotic distribution of the restricted maximum composite likelihood estimate.

Suggested Citation

  • N. Martín & L. Pardo & K. Zografos, 2019. "On divergence tests for composite hypotheses under composite likelihood," Statistical Papers, Springer, vol. 60(6), pages 1883-1919, December.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:6:d:10.1007_s00362-017-0900-1
    DOI: 10.1007/s00362-017-0900-1
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    References listed on IDEAS

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    1. Martin, Nirian & Mata, Raquel & Pardo, Leandro, 2016. "Wald type and phi-divergence based test-statistics for isotonic binomial proportions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 120(C), pages 31-49.
    2. Martin, Nirian & Mata, Raquel & Pardo, Leandro, 2014. "Phi-divergence statistics for the likelihood ratio order: An approach based on log-linear models," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 387-408.
    3. K. Zografos, 1998. "f-Dissimilarity of Several Distributions in Testing Statistical Hypotheses," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 295-310, June.
    4. Cristiano Varin, 2008. "On composite marginal likelihoods," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(1), pages 1-28, February.
    5. Morales, D. & Pardo, L. & Vajda, I., 1997. "Some New Statistics for Testing Hypotheses in Parametric Models, ," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 137-168, July.
    6. Hsinchun Chen & Yilu Zhou & Edna F. Reid & Catherine A. Larson, 2011. "Introduction to special issue on terrorism informatics," Information Systems Frontiers, Springer, vol. 13(1), pages 1-3, March.
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