Dipartimento di Scienze Statistiche

The use of auxiliary variables at the estimation stage is a wellestablished procedure in survey methodology. In the literature several estimators use them to improve the eciency of estimates. Generally, they include auxiliary variables through their exactly-known totals from register or administrative sources. However, increasingly also auxiliary variables with survey-estimated totals are taken into account to improve the estimates. In this situation, with both exactly-known and survey-estimated auxiliary totals, we present an optimal estimator following a complete design-based approach. The presented estimator can be seen as an extention of the Montanari (1987) optimal GREG estimator adapted to this situation. The expression of the estimator is derived for several cases that reect real situations. Moreover, a guideline to properly manage the survey-estimated auxiliary totals is given.