IASS Webinar 32: An extension of the weight share method when using a continuous sampling frame

27 September 2023; 2:00 - 3:30 PM CEST; 

Watch the video recording of this webinar here.

The definition of statistical units is a recurring issue in the domain of sample surveys. Indeed, not all the populations surveyed have a readily available sampling frame. For these populations, the sampled units are distinct from the observation units, which constitute the population of interest on which we are willing to infer. This issue has been raised for a long time for studying populations that are difficult to reach, e.g. homeless people.To deal with this issue, Deville and Lavallée (2006: Surv. Methodol., 32(2), 165-176) proposed the so-called weight share method. It is based on a principle of duality between the sampled population and the observed population, where a variable of interest defined on the observed population may be written as a synthetic variable defined on the sampling frame. Because it creates a link between the observation units and the sampling units, this method enables the properties of the sampling design to be used to define unbiased estimators of totals for the observed populations, and to derive variance formulas.This work deals with the extension of this method to the case when the sampled population is a continuous frame. We are particularly interested in applications encountered in forest inventories, in which it is common practice to use a sample of points selected in a continuum and then fixed-shape supports defined from these points to perform the survey on a discrete population of trees. The approach which consists of transporting a variable from the discrete population to the continuous population is not new, see for example Stevens and Urquhart (2000: Environmetrics, 11, 13-41) or Gregoire and Valentine (2007: CRC Press). However, the link between the units from the population sampled and the units of the target population are only implicit in these works. The weight share method is a very useful and simple tool to formalize this approach, and enables one to produce general formulas for both point estimators and variance estimators. We will present an application of this approach for formalizing estimation and variance estimation in the French National Forest Inventory. We will also present a possible application to spatial cluster sampling. This is based on joint work with Olivier Bouriaud (Université de Suceava, IGN), Philippe Brion (Irmar), Trinh Duong (IGN) and Minna Pulkkinen (IGN).