A single frame multiplicity estimator for multiple frame surveys

Multiple Frame Surveys were originally proposed to foster cost savings on the basis of an optimality approach. As surveys on special, rare and difficult-to-sample populations are becoming more prominent, a single list of population units to be used as a sampling frame is often unavailable in sampling practice. In recent literature multiple frame designs have been put forward in order to increase population coverage, improve response rates and capture differences and subgroups. Alternative approaches to multiple frame estimation have appeared, all of them relying upon the virtual partition of the set of the available overlapping frames into disjointed domains. Hence the correct classification of sampled units into the domains is required for practical applications. In this paper a multiple frame estimator is proposed using a multiplicity approach. Multiplicity estimators require less information about unit domain membership hence they are insensitive to misclassification. Moreover the proposed estimator is analytically simple so that it is easy to implement and its exact variance is given. Empirical results from an extensive simulation study comparing the multiplicity estimator with major competitors are also provided.