Pairwise conditional score functions: a generalization of the Mantel-Haenszel estimator

Pairwise conditional score functions are proposed and explored. They provide us with an interpretation on the Mantel-Haenszel estimator, and are applicable to deriving the Mantel-Haenszel-type estimators under the exponential dispersion model with multiple strata. Explicit forms of the estimating functions are presented, and the asymptotic relative efficiency is examined in the cases of the exponential and the geometric distributions. The derivation and the numerical results suggest that the derived estimators are fairly robust and show high efficiency as the Mantel-Haenszel estimator.