Tests for isotropy in spatial point patterns - A comparison of statistical indices

Isotropy of a point process, defined as invariance of the distribution under rotation, is often assumed in spatial statistics. Formal tests for the hypothesis of isotropy can be created by comparing directional summary statistics in different directions. In this paper, the statistical powers of tests based on a variety of summary statistics and several choices of deviance measures are compared in a simulation study. Four models for anisotropic point processes are considered covering both regular and clustered cases. We discuss the robustness of the results to changes of the tuning parameters, and highlight the strengths and limitations of the methods.