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Phi-divergence statistics for the likelihood ratio order: An approach based on log-linear models

Author

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  • Martin, Nirian
  • Mata, Raquel
  • Pardo, Leandro

Abstract

When some treatments are ordered according to the categories of an ordinal categorical variable (e.g., extent of side effects) in a monotone order, one might be interested in knowing whether the treatments are equally effective or not. One way to do that is to test if the likelihood ratio order is strictly verified. A method based on log-linear models is derived to make statistical inference and phi-divergence test-statistics are proposed for the test of interest. Focused on log-linear modeling, the theory associated with the asymptotic distribution of the phi-divergence test-statistics is developed. An illustrative example motivates the procedure and a simulation study for small and moderate sample sizes shows that it is possible to find phi-divergence test-statistic with an exact size closer to nominal size and higher power in comparison with the classical likelihood ratio.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:130:y:2014:i:c:p:387-408
    DOI: 10.1016/j.jmva.2014.06.004
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    References listed on IDEAS

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    1. Martín, Nirian & Pardo, Leandro, 2008. "New families of estimators and test statistics in log-linear models," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1590-1609, September.
    2. Martín, N. & Balakrishnan, N., 2013. "Hypothesis testing in a generic nesting framework for general distributions," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 1-23.
    3. Ori Davidov & Konstantinos Fokianos & George Iliopoulos, 2010. "Order-Restricted Semiparametric Inference for the Power Bias Model," Biometrics, The International Biometric Society, vol. 66(2), pages 549-557, June.
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    Citations

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    Cited by:

    1. Kateri, Maria & Nikolov, Nikolay I., 2022. "A generalized Mallows model based on ϕ-divergence measures," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    2. 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.
    3. 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.

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