Showing papers by "Barry Boots published in 1999"

A Variance-Stabilizing Coding Scheme for Spatial Link Matrices:

Abstract: In spatial statistics and spatial econometrics two coding schemes are used predominately. Except for some initial work, the properties of both coding schemes have not been investigated systematically. In this paper we do so for significant spatial processes specified as either a simulta-neous autoregressive or a moving average process. Results show that the C-coding scheme emphasizes spatial objects with relatively large numbers of connections, such as those in the interior of a study region. In contrast, the W-coding scheme assigns higher leverage to spatial objects with few connections, such as those on the periphery of a study region. To address this topology-induced heterogeneity, we design a novel S-coding scheme whose properties lie in between those of the C-coding and the W-coding schemes. To compare these three coding schemes within and across the different spatial processes, we find a set of autocorrelation parameters that makes the processes stochastically homologous via a method based on the ex...

Relaxing the nearest centre assumption in central place theory

Abstract: Although a variety of modifications of classical central place theory has been proposed, one area that remains unexplored is the effect of relaxing the nearest centre assumption for the purchase of a specified basket of goods within a given hierarchical level. This article examines the effect of such a relaxation on central place market areas by using higher-order Voronoi diagrams. When used to model market areas, higher-order Voronoi diagrams can be interpreted as overlapping and probabilistic regions. These diagrams construct market areas based on the assumption that consumers choose from a set of \(k (k = 1, 2, \ldots, n)\) nearest centres of the same hierarchical level. If consumers are assumed to be indifferent between the k centres, the appropriate market areas are given by the order-k Voronoi diagram. In this case, it is shown that sales potentials are consistent with those that result when the nearest centre assumption is in effect. If consumers are assumed to have a preference for nearer centres, market areas are defined by the ordered, order-k Voronoi diagram. This situation generates sales potentials which can vary between centres.

articles: Relaxing the nearest centre assumption in central place theory

Abstract: Although a variety of modifications of classical central place theory has been proposed, one area that remains unexplored is the effect of relaxing the nearest centre assumption for the purchase of a specified basket of goods within a given hierarchical level. This article examines the effect of such a relaxation on central place market areas by using higher-order Voronoi diagrams. When used to model market areas, higher-order Voronoi diagrams can be interpreted as overlapping and probabilistic regions. These diagrams construct market areas based on the assumption that consumers choose from a set of $k (k = 1, 2, \ldots, n)$ nearest centres of the same hierarchical level. If consumers are assumed to be indifferent between the k centres, the appropriate market areas are given by the order-k Voronoi diagram. In this case, it is shown that sales potentials are consistent with those that result when the nearest centre assumption is in effect. If consumers are assumed to have a preference for nearer centres, market areas are defined by the ordered, order-k Voronoi diagram. This situation generates sales potentials which can vary between centres.