Generalized Multiplicity-adjusted Horvitz-Thompson Estimation as a Unified Approach to Multiple Frame Surveys

The available multiple frame estimation methods do not deal with the case of mixed frame level information where unitS from the same sample are allowed to have mixed information. That is. some units may have only basic (possibly due to privac3 concerns or lack of memory on the pan of the respondent) while others na’ have more than basic information, where basic is defined as having known selection probability fir each unit from the sampled frame and the number of frames the unit could have been selected from but nut knowing the frame identification except. of course, for the sampled frame. To address this new problem, we first propose a unified approach based on multiplicityadjusted estimation which encompasses all the proposed estimators (classified in this article as either combined or separate) as well as new estimators obtained by combining simple and complex multiplicity estimators. We also propose hybrid multiplicity estimators to account for mixed inforniation. The methods discussed here are limited to the combined frame approach only because of their ability to deal with the case of mixed information. Simulation results are presented to compare various methods in lerms of relative bias and relative root mean squared error of point and variance estimators