In social and economic surveys, it can be diﬃcult to directly reach units of the target population, and indirect sampling is often advocated to solve this issue. In indirect sampling, the sample is drawn from a frame population that is linked to the target population, and estimation of tar-get population parameters is typically achieved through the Generalized Weight Share Method (GWSM). This method provides a weight, for every unit of the target population, that depends on the one hand, on the sam-pling weights in the frame population and, on the other hand, on the link weights between the frame population and the target population. In the present study, we focus on the situation in which the units from the frame population are linked to one and only one unit from the target population (Many-to-One case). This situation is encountered at the French postal service where addresses are sampled instead of postman rounds. We aim at understanding of the impact of the link weights on the eﬃciency of the GWSM estimators. We derive variance expressions and optimality results for a large class of sampling designs. Moreover, we note that the Many-to-One case can lead to too many links to observe. We alleviate the problem by introducing an intermediate population and double indirect sampling. The question of the loss of precision in this situation is discussed in detail through theoretical results and simulations. These ﬁndings help to ex-plain the loss of precision of double GWSM estimators observed recently at the French postal service.
Generalized Weight Share Method; Optimal link weights; Stratiﬁed sampling; Variance estimation;
Estelle Medous, Camelia Goga, Anne Ruiz-Gazen, Jean-François Beaumont, Alain Dessertaine et Pauline Puech, « Many-to-One indirect sampling with application to the French postal traffic estimation », TSE Working Paper, n° 21-1269, novembre 2021.
TSE Working Paper, n° 21-1269, novembre 2021