Consistent Estimation of Cross-Classified Domains

Domain estimation has become an important area in survey sampling, however a lot of problems associate with it. One out of many is the lack of consistency between different surveys. The results of one survey do not coincide with the results of another survey done earlier or simultaneously, although the same variable is under study. We study two methods, AC-calibration (A – auxiliary, C – common) and repeated weighting (RW), for achieving consistency. A short overview of these two methods is given, and we develop formulas for a specified case, for the crossclassified domains. We assume that there are two sources of information on the study variables (either surveys or registers). The problem is that one source has information on domains formed by certain categorical variable, not considered or not identified in the other source. Instead, this second source has information on domains formed by another categorical variable. We are however interested in domains cross-classified with these categorical variables. A survey is done regarding these new domains, but the domain estimates will probably be inconsistent with marginal information, from earlier surveys. We require that the new domain estimates be consistent with the marginals. To achieve this we apply AC-calibration or repeated weighting. The formulas of AC-calibration and RW for the cross-classified domains are tested in a simulation study. Simulations were done on a population composed of real data from the Estonian Household Survey.