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On the closure of relational models

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  • Klimova, Anna
  • Rudas, Tamás

Abstract

Relational models for contingency tables are generalizations of log-linear models, allowing effects associated with arbitrary subsets of cells in a possibly incomplete table, and not necessarily containing the overall effect. In this generality, the MLEs under Poisson and multinomial sampling are not always identical. This paper deals with the theory of maximum likelihood estimation in the case when there are observed zeros in the data. A unique MLE to such data is shown to always exist in the set of pointwise limits of sequences of distributions in the original model. This set is equal to the closure of the original model with respect to the Bregman information divergence. The same variant of iterative scaling may be used to compute the MLE whether it is in the original model or in its closure.

Suggested Citation

  • Klimova, Anna & Rudas, Tamás, 2016. "On the closure of relational models," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 440-452.
    • Handle: RePEc:eee:jmvana:v:143:y:2016:i:c:p:440-452
    DOI: 10.1016/j.jmva.2015.10.005
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    References listed on IDEAS

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    1. Evans, R.J. & Forcina, A., 2013. "Two algorithms for fitting constrained marginal models," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 1-7.
    2. Klimova, Anna & Rudas, Tamás & Dobra, Adrian, 2012. "Relational models for contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 159-173, February.
    3. Anna Klimova & Tamás Rudas, 2015. "Iterative Scaling in Curved Exponential Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 832-847, September.
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    Cited by:

    1. Klimova, Anna & Rudas, Tamás, 2022. "Hierarchical Aitchison–Silvey models for incomplete binary sample spaces," Journal of Multivariate Analysis, Elsevier, vol. 187(C).

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