March 2023 Many-to-One indirect sampling with application to the French postal traffic estimation
Estelle Medous, Camelia Goga, Anne Ruiz-Gazen, Jean-François Beaumont, Alain Dessertaine, Pauline Puech
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Ann. Appl. Stat. 17(1): 838-859 (March 2023). DOI: 10.1214/22-AOAS1653


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 target 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 sampling 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 explain the loss of precision of double GWSM estimators observed recently at the French postal service.

Funding Statement

This work has been partly supported by the French Agence Nationale de la Recherche through CIFRE contract 2019/1966 and through the Investments for the Future (Investissements d’Avenir) program, grant ANR-17-EURE-0010.


We would like to thank the Associate Editor and three reviewers who helped us improve the article.


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Estelle Medous. Camelia Goga. Anne Ruiz-Gazen. Jean-François Beaumont. Alain Dessertaine. Pauline Puech. "Many-to-One indirect sampling with application to the French postal traffic estimation." Ann. Appl. Stat. 17 (1) 838 - 859, March 2023.


Received: 1 November 2021; Revised: 1 June 2022; Published: March 2023
First available in Project Euclid: 24 January 2023

Digital Object Identifier: 10.1214/22-AOAS1653

Keywords: Generalized weight share method , optimal link weights , stratified sampling , variance estimation

Rights: Copyright © 2023 Institute of Mathematical Statistics


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Vol.17 • No. 1 • March 2023
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