Approximately optimum strata boundaries for two concomitant stratification variables under proportional allocation

The proper choice of strata boundaries is an important factor determining the efficiency of the estimator of the considered characteristics of a population. In this article, the Cum Di(x,z) Rule (i=3,4) for obtaining approximately optimum strata boundaries has been applied, taking into account a single-study variable along with two concomitant variables serving as the basis of the stratification variables. The relative efficiency of the proposed methods has been demonstrated theoretically and empirically by comparing them to a selection of already-existing methods in a simulation study with the use of the proportional allocation method.