Design-based Estimators Calibrated on Estimated Totals from Multiple Surveys

The use of auxiliary variables to improve the efficiency of estimators is a well-known strategy in survey sampling. Typically, the auxiliary variables used are the totals of appropriate measurement that are exactly known from registers or administrative sources. Increasingly, however, these totals are estimated from surveys and are then used to calibrate estimators and improve their efficiency. We consider different types of survey structures and develop design-based estimators that are calibrated on known as well as estimated totals of auxiliary variables. The optimality properties of these estimators are studied. These estimators can be viewed as extensions of the Montanari generalised regression estimator adapted to the more complex situations. The paper studies interesting special cases to develop insights and guidelines to properly manage the survey-estimated auxiliary totals.