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The Joint Asymptotic Distribution of the Maximum Likelihood and Mantel-Haenszel Estimators of the Common Odds Ratio in k 2 x 2 Tables

In: Modelling and Prediction Honoring Seymour Geisser

Author

Listed:
  • Samuel W. Greenhouse

    (The George Washington University, Department of Statistics)

  • Joseph L. Gastwirth

Abstract

The Mantel-Haenszel (MHE) and Maximum Likelihood (MLE) estimators of an assumed common odds ratio in the analysis of several (k) 2x2 tables are usually found to be quite close. This suggests their joint asymptotic distribution should have a high correlation. Since the MLE cannot be obtained as an explicit function of the observations, we instead utilize an asymptotically equivalent surrogate for the MLE enabling us to find a large sample representation for the two estimators from which we obtain their joint asymptotic distribution. This is found for both the uncondtional and conditional likelihoods, under the assumption that k is fixed and the sample sizes within each table approach infinity.

Suggested Citation

  • Samuel W. Greenhouse & Joseph L. Gastwirth, 1996. "The Joint Asymptotic Distribution of the Maximum Likelihood and Mantel-Haenszel Estimators of the Common Odds Ratio in k 2 x 2 Tables," Springer Books, in: Jack C. Lee & Wesley O. Johnson & Arnold Zellner (ed.), Modelling and Prediction Honoring Seymour Geisser, pages 264-273, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2414-3_16
    DOI: 10.1007/978-1-4612-2414-3_16
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