Spatial dependence measures based on two parametric semivariogram perspectives

Abstract

On studying the semivariogram, there is the possibility of estimating descriptive measures of spatial dependence degree. In this study, we aimed to show two spatial dependence measures developed from two distinct geometric perspectives of the semivariogram. The first measure, named IDE1, is based on the concept of spatial dependence areas found in the semivariogram; while the second, named IDE2, is based on the concept that the semivariogram has two distinct areas, an of spatial dependence, and other of non-spatial dependence. The IDE1 is identical to the DE index found in the literature, so that it is possible to state that the mathematical proof of the DE index was from the geometry of semivariogram. The IDE2 is more complete than the IDE1 index because it considers the factor of model, showing that there are differences in spatial dependence of phenomena obtained from their relating models. These two indices do not contemplate the practice reach. Thus, we may consider that the estimates of IDE1 and IDE2 may be used to describe the spatial dependence; however, they should be used along with other measures which contemplate the reach of the spatial dependence.