Inspired by Art

The research of Art Getis has had many positive direct effects on the fields of regional science and spatial statistics. There already have been, and will continue to be, many indirect effects as well, as the repercussions of his work ripple through the field. With his contributions to spatial statistics, Art Getis laid out a rich research agenda for future work in the field. In this presentation, I describe several research problems inspired by his work. These include (a) the multiple testing problem, (b) the effects of global spatial autocorrelation on the power and use of local statistics, (c) the effects of weight misspecification on the power of local statistics, and (d) the statistical distribution of his local spatial heterogeneity (LOSH) statistic. In addition, there are a number of connections between the local statistics he developed and other statistics. These include the relationships between (a) the Getis-Ord statistic and the two-sample t statistic, (b) the Getis-Ord statistic and the maximum of Gaussian random fields, and (c) the LOSH statistic and the well-known Geary statistic.