Testing local spatial autocorrelation using k-order neighbours

The analysis of local spatial autocorrelation for spatial attributes has been an important concern in geographical inquiry. In this paper, we propose a concept and algorithm of k-order neighbours based on Delaunay's triangulated irregular networks and redefine Getis and Ord's (1992) local spatial autocorrelation statistic as G(i)(k) with weight coefficient w(ij)(k) based on k-order neighbours for the study of local patterns in spatial attributes. To test the validity of these statistics, an experiment is performed using spatial data of the elderly population in Ichikawa City, Chiba Prefecture, Japan. The difference between the weight coefficients of the k-order neighbours and distance parameter to measure the spatial proximity of districts located in the city centre and near the city limits is found by Monte-Carlo simulation.