On pixel-based regression: aspects of statistical modelling, estimation and model structure

We employ statistical methodology to investigate techniques used in Geographical Information Systems (GIS) to analyse point pattern data. In modelling such data, statisticians would usually apply well-known spatial point process methods to the exact spatial coordinates of the points. By contrast, the first step taken in GIS applications is often to discretise the point pattern. We develop the theories of estimating functions, and estimation in mis-specified models. This enables appropriate examination of performances of common pixel-based regression techniques and motivates the study of some variants. Consideration of the model structures gives rise to easier derivations and interpretations of the results.