Generalised regression is the most common design-based model-assisted method for estimation
of population means and totals in practical survey sampling. However, it is often unacceptable
in the context of small area estimation, where one is interested in population means and totals for
a large number of areas (or domains) and the sample sizes are either small or non-existent in
many of them. In this seminar, we discuss an approach to extend generalised regression from
direct estimation for the whole population to indirect estimation of all the small area populations.
This requires to trade variance off with bias and enables a practical methodology for estimation
at the different aggregation levels, which is coherent numerically (self-benchmarking) as well as
conceptually in terms of the design-based model-assisted inference outlook. Estimation can be
conducted by means of an *extended* weighting system that has as many sets of weights as the
number of small areas: each set produces the estimate for a domain mean of one or more survey
variables of interest and is, in this sense, multipurpose.
27 Maggio 2022
Maria Giovanna Ranalli
Università degli Studi di Perugia