The effect of alternative measures of distance on distance-weighted smoothing for spatial dat

This dissertation demonstrates the use of alternative measures of distance in distance-weighted smoothing techniques. It focuses on application scenarios where the spatial sample space is represented by regular and random tessellations. This dissertation develops a methodology using alternative measures of distance that addresses the existence of spatial boundaries within the sample space. These distance measures are non-Euclidean in nature and accommodate path constraints such as boundaries, gaps, edges, and barriers. These alternative measures are based on the idea that distance between two points in a spatial sample space is equivalent to the length of a possible path between the two locations.;This dissertation examines the mathematically properties of the alternative measures to show that they provided a reasonable measure of distance. These types of alternative distance measures are computationally complex. Therefore, an important aspect of this dissertation was to develop an efficient algorithm for computing the alternative distance. This dissertation uses simulation to examine the relative effectiveness of the alternative distance measure for 3 distance-weighted smoothing techniques-kernel estimation, locally weighted regression, and kriging. For kernel estimation and locally weighted smoothing the simulation indicates that alternative measures provide a better basis for smoothing when boundaries are present and competitive with Euclidean procedures when there are no internal boundaries. The notion of boundaries is not compatible with the assumptions behind kriging and computation problems often result when attempts are made to use alternative distance in the kriging process. Thus kriging and alternative distance measures are applicable to separate classes of smoothing problems.