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New families of estimators and test statistics in log-linear models

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  • Martín, Nirian
  • Pardo, Leandro

Abstract

In this paper we consider categorical data that are distributed according to a multinomial, product-multinomial or Poisson distribution whose expected values follow a log-linear model and we study the inference problem of hypothesis testing in a log-linear model setting. The family of test statistics considered is based on the family of [phi]-divergence measures. The unknown parameters in the log-linear model under consideration are also estimated using [phi]-divergence measures: Minimum [phi]-divergence estimators. A simulation study is included to find test statistics that offer an attractive alternative to the Pearson chi-square and likelihood-ratio test statistics.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:8:p:1590-1609
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    References listed on IDEAS

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    1. N. Martín & L. Pardo, 2008. "Minimum phi-divergence estimators for loglinear models with linear constraints and multinomial sampling," Statistical Papers, Springer, vol. 49(1), pages 15-36, March.
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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, 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. Martín, Nirian, 2015. "Diagnostics in a simple correspondence analysis model: An approach based on Cook’s distance for log-linear models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 175-189.

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