Introduction

In survey sampling, some populations are hard to reach because they happen to be hard to survey. Their relative rareness and the absence of a suitable sampling frame are two main reasons for this. As mentioned by Kalton and Anderson (1986): “The initial consideration in designing a sample for a rare population is whether there exists a separate frame for that population. If a separate frame exists, is available for sample selection and is deemed adequate, the sample may be selected from it using standard methods and no problems arise.” When no sampling frame is available for the desired target population, one might then choose a sampling frame that is indirectly related to the targeted rare population. We can then speak of two populations UA and UB that are related to one another. We wish to produce an estimate for the population UB by selecting a sample from the population UA for which a sampling frame is available and using the existing links between the two populations. This sampling process is referred to as indirect sampling (Lavallée, 2002, 2007). Producing estimates in the context of indirect sampling can be difficult to achieve if the links between UA and UB are not one-to-one. A solution for this is to use the generalized weight share method (GWSM).

The population UB can be the hard-to-survey population itself or it can be a population that contains it as a subpopulation. Fortunately for the statistician, it turns out that hard-to-reach populations can often be found by surveying clusters. This is the case, for example, with infectious diseases (Thompson, 1992). In this chapter then, we will assume that the population UB is partitioned into clusters. Selection of clusters will then be performed through the indirect sampling process. Since sampling clusters rather than individual units might allow easier tracking of units that are part of the hard-to-reach populations, we can foresee considerable reductions in costs since a large part of the costs are related to the identification of the hard-to-reach populations. As well, cluster sampling allows for the production of results at the cluster level itself, in addition to the units.