Assessing Spatial Isotropy

This chapter proposes an objective test of the isotropy assumption that applies to a large class of spatial structures. In a spatial data analysis the analyst typically requires knowledge of the underlying correlation structure in order to effectively model data. A common assumption for this structure is one of isotropy, the direction independent correlation. While graphical techniques are useful to check for isotropy, they are often difficult to assess and cannot be interpreted objectively. Specifically, no explicit knowledge of marginal or joint distributions of the process is necessary, and the shape of the random field can be quite irregular. It is found that a test for isotropy may be obtained by comparing semivariograms at lags with the same length but in different directions. As the semivariograms are typically unknown, a test is formed based on estimators of the semivariograms. In the nonparametric spirit, the strength of dependence in the random field is quantified by a model-free mixing condition.