Methodological Principles for a Generalized Estimation System at Statistics Canada
V. Estevao, M.A. Hidiroglou, and C.E. Sa¨rndal
In this paper we present the methodological principles behind the development of the Generalized Estimation System (GES) at Statistics Canada. The GES allows the specification of an estimator from a wide group of estimators produced under a general linear regression model. The resulting GREG estimators are characterized in the paper via three important concepts: model level, model groups and the model type. Familiar estimators such as the simple expansion, post-stratified and raking ratio estimators can be classified according to these concepts. But more generally, these concepts help to structure a wide class of possible estimators. The specification of a GREG model depends on the available auxiliary totals. This information is used to produce a set of g-factors to adjust the sample design weights. The resulting final weights have the property of producing estimates for the auxiliary variables which are equal to the known auxiliary totals. This consistency condition is appealing to most survey practitioners. Furthermore, efficient estimates are produced when the variable of interest is highly correlated with the auxiliary variables. The GES produces domain estimates for parameters such as domain size, totals, ratios of totals and means. This is done based on the sample design and the specified GREG model. We have shown that it is possible to extend the theory for the estimation of a total to handle any non-linear parameter. This is done through the usual Taylor approximation. Variance estimation is based on a formula suggested by Sa¨rndal, Swensson, and Wretman which incorporates both the g-weights and the residuals under the specified model.
Generalized regression estimator; auxiliary information; model groups; model level; model type.