The combination of several socio-economic data bases originating from
different administrative sources collected on several different partitions of a
geographic zone of interest into administrative units induces the so called
areal interpolation problem. This problem is that of allocating the data from a
set of source spatial units to a set of target spatial units. A particular case
of that problem is the re-allocation to a single target partition which is a
regular grid. At the European level for example, the EU directive 'INSPIRE', or
INfrastructure for SPatial InfoRmation, encourages the states to provide
socio-economic data on a common grid to facilitate economic studies across
states. In the literature, there are three main types of such techniques:
proportional weighting schemes, smoothing techniques and regression based
interpolation. We propose a stochastic model based on Poisson point patterns to
study the statistical accuracy of these techniques for regular grid targets in
the case of count data. The error depends on the nature of the target variable
and its correlation with the auxiliary variable. For simplicity, we restrict
attention to proportional weighting schemes and Poisson regression based
methods. Our conclusion is that there is no technique which always dominates