A Single-Frame Multiplicity Estimator for Multiple Frame Survey

Multiple Frame Survey has been originally proposed, according to an optimality approach, in order to persecute survey cost savings, especially in the case of a complete list available but expensive to sample. In the modern sampling practice it is frequent the case where a total and up-to-date list of units, to be used as sampling frame, is not available or it may not be built unless expensive or unfeasible screening of the target population. Instead, a set of lists singularly partial, usually overlapping, with union offering an adequate coverage of the target population, can be available. Thus the collection of the partial lists can be used as Multiple Frame. Literature about Multiple Frame estimation theory mainly concentrates over the Dual Frame case and it is only rarely concerned with the important practical issue of the variance estimation. By using a multiplicity approach a Single Frame estimator is proposed. The new estimator naturally applies to any number of frame and it is very simple so that its variance is given exactly and easily estimated.