Optimal weighted estimation versus Cochran-Mantel-Haenszel

The purpose of this paper is to contrast the Mantel-Haenszel estimator with an optimal estimator to better understand its specific nature, as well as some unique and interesting properties of the data setting for which it was developed. It is emphasized here that the Mantel-Haenszel estimator does not follow from optimality considerations, but nevertheless has properties similar to and often better than the optimal estimator, whose existence we demonstrate in spite of the absence of completeness. It is shown, via simulations and data analysis, that the optimal estimator outperforms the Mantel-Haenszel estimator only in certain settings with huge sample sizes.