Accuracy of areal interpolation methods for count data

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. 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 processes to study the statistical accuracy of these techniques for regular grid targets in the case of count data. For simplicity, we restrict attention to count related target variables, proportional weighting schemes and Poisson regression based methods. The error depends on many factors including the relative size of the targets with respect to the sources, the homogeneity of the auxiliary information variables and the relative importance of the different auxiliary information in the mean target values. Our conclusion is that there is no technique which always dominates at finite distance but that asymptotically the pycnophylactic Poisson regression is the best feasible method among the ones considered.