Several strategies for resolving geographic boundary problems in measurement and analysis have been proposed.Martin, R. J. (1987) Some comments on correction techniques for boundary effects and missing value techniques. Geographical Analysis 19, 273–282.Wong, D. W. S., and Fotheringham, A. S. (1990) Urban systems as examples of bounded chaos: exploring the relationship between fractal dimension, rank-size and rural-to-urban migration. Geografiska Annaler 72, 89–99. To identify the effectiveness of the strategies, Griffith reviewed traditional techniques that were developed to mitigate the edge effects: ignoring the effects, undertaking a torus mapping, construction of an empirical buffer zone, construction of an artificial buffer zone, extrapolation into a buffer zone, utilizing a correction factor, etc. The first method (i.e., the ignorance of the edge effects), assumes an infinite surface in which the edge effects do not occur. In fact, this approach has been used by traditional geographical theories (e.g., central place theory). Its main shortcoming is that empirical phenomena occur within a finite area, so an infinite and homogeneous surface is unrealistic. The remaining five approaches are similar in that they attempted to produce unbiased parameter estimation, that is, to provide a medium by which the edge effects are removed. (He called these operational solutions as opposed to statistical solutions to be discussed below.) Specifically, the techniques aim at a collection of data beyond the boundary of the study area and fit a larger model, that is, mapping over the area or over-bounding the study area.Ripley, B. D. (1979) Tests of "randomness" for spatial point patterns. Journal of the Royal Statistical Society, Series B 41, 368–374. Through simulation analysis, however, Griffith and Amrhein identified the inadequacy of such an overbounding technique. Moreover, this technique can bring about issues related to large-area statistics, that is, ecological fallacy. By expanding the boundary of the study area, micro-scale variations within the boundary can be ignored.
