Читать книгу Sampling and Estimation from Finite Populations - Yves Tille - Страница 19

The “superpopulation” approach has led to extremely fruitful research. The development of a hybrid approach called the model‐assisted approach allows valid inferences to be provided under the model but is also robust when the model is wrong. This view was mainly developed by a Swedish school (see Särndal et al., 1992). The model allows us to take into account auxiliary information at the time of estimation while preserving properties of robustness for the estimators in the event of nonadequacy of the model. It is actually very difficult to construct an estimator that takes into account a set of auxiliary information after the selection of the sample without making a hypothesis, even a simple one, on the relation existing between the auxiliary information and the variable of interest. The modeling allows a conceptualization of this type of presumption. The model‐assisted approach allows us to construct interesting and practical estimators. It is now clear that the introduction of a model is a necessity for dealing with some nonresponse and estimation problems in small areas. In this type of problem, whatever the technique used, one always postulates the existence of a model even if sometimes this is implicit. The model also deserves to be clearly determined in order to explain the underlying ideas that justify the application of the method.