In this paper we specify, within a hierarchical Bayesian setting, appropriate atom-based
models to solve the following small area estimation (SAE) questions: (i) combining
auxiliary covariates which are available on non nested areal partitions (misaligned areal
regression problem); (ii) providing small area estimates by using planned domains data
(misaligned areal interpolation problem). To illustrate our approach we consider the
problem of estimating the number of unemployed at Local Labour Market area (small
area or target zone) level by using two misaligned source data: auxiliary information
available on different administrative partitions; reliable estimates of unemployed on
Labour Force Survey planned domains. Thus we explore the close connection that
typical SAE issues show to have with spatial misalignment problems. Ob ject of SAE
is, in fact, inference on survey non-planned “minor domains” (the so called small areas):
based on direct domain data (when available), it leads to estimates of poor quality.
Thereby models are set up for borrowing strength from indirectly related data sources.
Similarly, spatial misalignment models are set up whenever “target zones” for which
data are needed are different from source zones on which data are available.
