Indirect sampling: The foundations of the generalized weight share method - ARCHIVED

To select a survey sample, it happens that one does not have a frame containing the desired collection units, but rather another frame of units linked in a certain way to the list of collection units. It can then be considered to select a sample from the available frame in order to produce an estimate for the desired target population by using the links existing between the two. This can be designated by Indirect Sampling.

Estimation for the target population surveyed by Indirect Sampling can constitute a big challenge, in particular if the links between the units of the two are not one-to-one. The problem comes especially from the difficulty to associate a selection probability, or an estimation weight, to the surveyed units of the target population. In order to solve this type of estimation problem, the Generalized Weight Share Method (GWSM) has been developed by Lavallée (1995) and Lavallée (2002). The GWSM provides an estimation weight for every surveyed unit of the target population.

This paper first describes Indirect Sampling, which constitutes the foundations of the GWSM. Second, an overview of the GWSM is given where we formulate the GWSM in a theoretical framework using matrix notation. Third, we present some properties of the GWSM such as unbiasedness and transitivity. Fourth, we consider the special case where the links between the two populations are expressed by indicator variables. Fifth, some special typical linkages are studied to assess their impact on the GWSM. Finally, we consider the problem of optimality. We obtain optimal weights in a weak sense (for specific values of the variable of interest), and conditions for which these weights are also optimal in a strong sense and independent of the variable of interest.