Evaluation of Accuracy of Aveal Interpolation

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Integration of spatial data requires a data transfer from one zonal system to another. This process is given the term "areal interpolation" which implies spatial interpolation based on areal data, in contrast to "point interpolation" or simply "interpolation" which estimates a surface using data collected at sample points. Areal interpolation is inevitably uncertain to some extent because it involves data estimation based on arbitrary assumptions on the distribution of spatial objects. Hence, in order to improve estimation accuracy, numerous areal interpolation methods have been proposed in the literature.Along with the development of new methods, there has arisen a need for comparison of estimation accuracy between interpolation methods. To meet this demand, geographers have recently compared the accuracy of areal interpolation methods. Langford et al. (1991) investigated the accuracy of three areal interpolation methods. They estimated the population distribution of northern Leiceste … More rshire by regression models where landuse data were used as independent variables. Goodchild et al. (1993) proposed an interpolation method using ancillary data called "control zones" in which population density was reasonably assumed to be constant. They employed seven interpolation methods including their new method to estimate the population of counties in California and compared the accuracy of estimates.In this research we propose a theoretical framework for comparison of estimation accuracy among areal interpolation methods. Our approach is based on a stochastic model that represents diverse geographic situations, and the model requires far less computational cost than Monte Carlo simulation does. In addition to this advantage, it allows us to discuss theoretically the relationship between estimation accuracy and areal interpolation methods. The model is used to examine the relationship between estimation accuracy and the spatial distribution of estimation error from a theoretical viewpoint. The analysis shows that the uniformity in error distribution improves the accuracy of areal interpolation. Four areal interpolation methods are then assessed through numerical examinations. From this it is found that the accuracy of simple interpolation methods heavily depends on the appropriateness of their hypothetical distributions, whereas the accuracy of intelligent methods depends on the fitness of the range of supplementary data for that of true distribution. Less