Evaluation of Accuracy of Aveal Interpolation

空间数据的整合需要将数据从一个分区系统转移到另一个分区系统。这个过程被称为"区域插值"，这意味着基于区域数据的空间插值，与"点插值"或简单的"插值"相反，"插值"使用在采样点收集的数据来估计表面。面积插值不可避免地具有一定程度的不确定性，因为它涉及基于对空间对象分布的任意假设的数据估计。因此，为了提高估计精度，在文献中提出了许多面积插值方法。沿着新方法的发展，出现了对插值方法之间的估计精度进行比较的需要。为了满足这一需求，地理学家最近比较了面积插值方法的精度。Langford等人（1991）研究了三种面积插值方法的精度。他们估计了莱切斯特北方的人口分布 ...更多信息 rshire的回归模型，其中土地利用数据作为自变量。Goodchild等人（1993年）提出了一种使用称为"控制区"的辅助数据的插值方法，其中人口密度被合理地假设为常数。他们使用了包括他们的新方法在内的七种插值方法来估计加州各县的人口，并比较了估计的准确性。我们的方法是基于一个随机模型，代表不同的地理情况下，该模型所需的计算成本远远低于蒙特卡洛模拟。除了这个优点之外，它允许我们从理论上讨论估计精度和面积插值方法之间的关系。该模型被用来从理论上研究估计精度和估计误差的空间分布之间的关系。分析表明，误差分布的均匀性提高了面插值的精度。四个面积插值方法，然后通过数值试验进行评估。由此可以发现，简单插值方法的精度在很大程度上取决于其假设分布的适当性，而智能方法的精度取决于补充数据的范围对真实分布的适合性。少

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