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The association between two random elements: A complete characterization and odds ratio models

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  • Gerhard Osius

Abstract

For random elements X and Y (e.g. vectors) a complete characterization of their association is given in terms of an odds ratio function. The main result establishes for any odds ratio function and any pre-specified marginals the unique existence of a corresponding joint distribution (the joint density is obtained as a limit of an iterative procedure of marginal fittings). Restricting only the odds ratio function but not the marginals leads to semi-parmetric association models for which statistical inference is available for samples drawn conditionally on either X or Y. Log-bilinear association models for random vectors X and Y are introduced which generalize standard (regression) models by removing restrictions on the marginals. In particular, the logistic regression model is recognized as a log-bilinear association model. And the joint distribution of X and Y is shown to be multivariate normal if and only if both marginals are normal and the association is log-bilinear. Copyright Springer-Verlag 2004

Suggested Citation

  • Gerhard Osius, 2004. "The association between two random elements: A complete characterization and odds ratio models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(3), pages 261-277, November.
    • Handle: RePEc:spr:metrik:v:60:y:2004:i:3:p:261-277
    DOI: 10.1007/s001840300309
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    Cited by:

    1. Hua Yun Chen & Daniel E. Rader & Mingyao Li, 2015. "Likelihood Inferences on Semiparametric Odds Ratio Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1125-1135, September.

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