Following the classical sampling theory, the survey statistician selects samples of people, businesses or others, in order to obtain the desired information. Drawing the samples is usually done by randomly selecting from a list representing the target population. In practice, this list is often not available. At best, the statistician only has access to a different list, indirectly related to the targeted population.

The example of a survey of children where the statistician only has a list of adult persons is a typical case. In this case, the statistician first draws a sample of...