Testing for Spatial Independence Using Similarity Relations

In this article, we construct new, simple, and nonparametric tests for spatial independence using symbolic analysis. An important aspect is that the tests are free of a priori assumptions about the functional form of dependence, making them especially suitable in situations where the dependence is nonlinear. We define the concept of a similarity relation, which is used to keep track of similarity between neighboring observations. This similarity count is used to construct new statistical tests based on both random permutation simulations and derived asymptotic distributions. We include a M onte C arlo study to better illustrate the properties and the behavior of the new tests under several synthetically generated processes. Apart from being competitive compared with other nonparametric and parametric tests, results underline the outstanding power of the new tests for nonlinear‐dependent spatial processes.