The objective of this research is to develop statistical tests for some important properties of stationary spatial random fields. The properties to be considered are those of direction- invariance (isotropy) and separability, and variations thereof, of the second-order variation. In addition to having important scientific meaning in many situations, these properties, when they hold, can greatly simplify both the computations involved in, and conclusions made from, the analysis of spatial data. Parametric testing approaches, which are based on a parametric model for the semivariogram or covariance function, and nonparametric approaches, which utilize method-of-moments estimators for sempiparametric approach will also receive attention. Biological environmental, and physical scientists who analyze spatial data will find the testing procedures useful. The objective of this research is to develop statistical tests for some important properties of stationary spatial random fields. The properties to be considered are those of direction- invariance (isotropy) and separability, and variations thereof, of the second-order variation. This work will have potential impact on fields of biological, environmental and physical sciences.
