Single frame estimation in multiple frame surveys

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 one complete and up-to-date list of units, to be used as sampling frame, is not available. Instead, a set of two or more lists singularly partial, usually overlapping, with union offering 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 fixed weights Single Frame estimator for Multiple Frame Survey is proposed. The new estimator naturally applies to any number of frames and requires no information about unit domain membership. Furthermore it is analytically simple so that its variance is given exactly and easily estimated. A simulation study comparing the new estimator with the major Single Frame competitors is also presented.