An empirical study of round and block norms for modelling actual distances

Abstract

<p>In this dissertation, we look at two families of distance predicting functions, the ℓkpθ norm family and the block norm family, that can be used for modelling actual distances. To compare the distance-predicting accuracy of the two families, an empirical study is conducted. Two types of regions, which are large geographic regions and urban centres, are used in the study. In the large geographic regions, actual distances between cities in each region are modelled, whereas in the urban centres, actual distances within a city are modelled. To evaluate the accuracy of the different norms, two goodness-of-fit criteria are employed. For the block norms, new procedures that determine global solutions for the criteria are developed. Normality assumptions regarding the individual terms of the criteria are examined since these terms are used to formulate statistical tests that are sensitive to departures from normality. A new criterion for evaluating the accuracy of a distance predicting function is developed. This criterion, unlike the other two criteria, is impartial both to short actual distances and to long actual distances. The criterion is used to evaluate the accuracy of the ℓkpθ norm for the geographic regions that were used in the empirical study. A statistical analysis of the errors from this new criterion leads to the development of confidence intervals for unknown distances in any geographic region. The results from this thesis will help an analyst select an appropriate distance predicting function to model actual distances in any application. Further, a new measure for evaluating distance predicting functions may be considered by an analyst, and confidence intervals for unknown distances can be easily constructed.</p>