Multiple Frame Surveys: a unified principled framework to estimation

The use of 2 or more sampling frames, possibly partial and overlapping, is often ad- vocated to improve population coverage, e.g. in telephone surveys or when dealing with difficult-to-sample-populations. Independent selections from multiple frames can also help reducing survey costs and offer flexibility by allowing to blend differ- ent sampling designs and data collection modes in different frames. However multiple frame (MF) surveys are challenging at the estimation stage. In fact if the possible overlap among the frames used in the survey allows for avoiding resource-consuming as well as error-prone screening operations, at the same time it allows for multiple opportunities of selection of the same unit in the final sample, whether or not sample duplications actually have occured. As a consequence, the increased inclusion prob- abilities for units included into more than one frame must be dealt with in efficient estimation of population parameters. Several methods have appeared in the litera- ture since Hartley first introduced Dual and MF surveys in the 60’s [1], each under a somewhat different approach leading to different level of complexity and information needs in order to be implemented in practice. A systematic and unified principled framework to MF estimation will be illustrated, based on the multiplicity approach, on the Generalized Multiplicity-adjusted HT class (GMHT) of MF estimators [2] as well as on the amount of frame-level meta-data available for estimation purposes. The potential of the multiplicity approach as a unified principled approach to MF estimation will be discussed, by casting all the existing MF estimators into a unique class. By using auxiliary info derived from the post-stratification of frame-samples into disjoint domain-samples, a regression rapresentation leading to a GMHT-reg class will be illustrated. New proposals emerging in the process as well as future research perspective will conclude. The talk is based on recent developments of joint work with A.C Singh (Center of Excellence in Survey Sampling, NORC @University of Chicago) and summarizes the three most recent joint papers [3], [4], [5].