Monitoring global spatial statistics

The use of global statistics to assess spatial dependence and deviations from spatial randomness often is carried out on a single dataset. However, there are situations where new datasets become available periodically, and it is of interest to determine whether there has been a temporal change point, where a new regime of global spatial autocorrelation has been established. If the global test is simply repeated every time period, change will be often be found by chance alone, even when it has not occurred, due to the multiple hypothesis testing. Cumulative sum methods are introduced as a method for monitoring the global statistics; they address the problem of multiple testing, and are optimal for finding temporal changes in the global spatial statistics. The method is illustrated through an application to data on breast cancer mortality in the northeastern United States.