Indirect Sampling (review)

The book has its roots in a doctoral dissertation that was completed in June 2001 at the Université Libre de Bruxelles, Belgium. The dissertation, perhaps a revision of it, appeared as a book in French, Le sondage indirect, ou la méthode généralisée du portage des poids, which was published simultaneously by Éditions de l'Université de Bruxelles (Belgium), and Éditions Ellipse (France) in 2002. The current book is an English-translation of the French version with 'some sections added to reflect the new developments that have occurred since 2002'.

In the more common (direct) sampling, a random sample of individuals is drawn from lists known as sampling frames representing the target population - the set of individuals under investigation. In such a case, individuals are selected with known probabilities of selection and these probabilities can be used to obtain the reliability of the information produced by the survey.

The need for indirect sampling arises when there is no sampling frame for the target population - a situation that, according to the author, is very common even in National Statistical Offices. Thus, the main motive of the book is to propose and develop techniques of getting valuable information and reliable estimates on the target population with no access to it but using a sampling frame of a population that is related to it.

A typical example is when one is interested to conduct a survey on children. Since a sampling frame of children may not be available one has to resort to adults - a population related to the target population (children) and for which sampling frame is available. Thus, a sample of adults is drawn from the available sampling frame, and all the children of the selected adults are surveyed. Here, a tacit assumption is that all children have at least one selectable parent. The book also provides a second example where indirect sampling may be more problematic: when only a list of businessmen and businesswomen is available a survey of businesses becomes complicated because a business person may own more than one business or that a business may be owned by more than one person.

The book is divided into ten chapters presenting theory, algorithms, and applications; as well treating difficulties brought by auxiliary information, non-response, or by the combination of different sources using record linkage.

The introductory chapter begins with a brief description of sampling theory and cluster sampling, and introduces indirect sampling, together with the associated weighting method - the Generalised Weight Share Method (GWSM). The GWSM is described at greater length in Chapter 2 and its merits are highlighted in connection with indirect sampling for rare populations, weighting using only selection probabilities of the selected units, weighting of populations related by complex links, and weighting of unlinked units. Chapter 3 is devoted to a brief review of the literature related to the foundations of GWSM - including Fair Share Method and its generalisation, Network Sampling, Adaptive Cluster Sampling, and Snowball Sampling.

Properties of the estimator based on GWSM are outlined in Chapter 4. It is shown that the estimator is unbiased and a formula for its variance is provided together with a method for its estimation. Further, it is shown that under conventional cluster sampling the GWSM estimator yields the same results as those obtained in classical theory. Since the GWSM estimator of the total is not guaranteed to have the smallest variance, the chapter ends with a description of a procedure for variance reduction. The procedure is based on obtaining optimal weighted links and then applying the well familiar Rao-Blackwell theorem - conditioning an unbiased estimator on a sufficient statistic in order to obtain a new estimator with at most equal variance as the unbiased estimator.

The GWSM estimator may be viewed as a generalisation of weight share method, network sampling, or snowball sampling. It is further generalised to two-stage sampling in Chapter 5, which also includes a discussion on the arbitrary aspect of cluster-formation and possibility of eliminating the notion of clusters. An application to...