Many-to-One indirect samplingwith application to the French postaltraffic estimation

Estelle Medous, Camelia Goga, Anne Ruiz-Gazen, Jean-François Beaumont, Alain Dessertaine and Pauline Puech
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Estelle Medous: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Camelia Goga: LMB - Laboratoire de Mathématiques de Besançon (UMR 6623) - CNRS - Centre National de la Recherche Scientifique - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE]
Jean-François Beaumont: Statistics Canada - Statistics Canada
Alain Dessertaine: Groupe La Poste
Pauline Puech: Groupe La Poste

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Abstract: 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 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.

Keywords: Generalized Weight Share Method; Optimal link weights; Stratified sampling; Variance estimation (search for similar items in EconPapers)
Date: 2023
Note: View the original document on HAL open archive server: https://hal.science/hal-04067663v1
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Published in Annals of Applied Statistics, 2023, 17 (1), pp.838-859. ⟨10.1214/22-AOAS1653⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04067663

DOI: 10.1214/22-AOAS1653

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