Several hypothesis testing methods have been proposed to validate the assumption of isotropy in spatial point patterns. A majority of these methods are characterised by an unknown distribution of the test statistic under the null hypothesis of isotropy. Parametric approaches to approximating the distribution involve simulation of patterns from a user-specified isotropic model. Alternatively, nonparametric replicates of the test statistic under isotropy can be used to waive the need for specifying a model. In this paper, we first develop a general framework which allows for the integration of a selected nonparametric replication method into isotropy testing. We then conduct a large simulation study comprising application-like scenarios to assess the performance of tests with different parametric and nonparametric replication methods. In particular, we explore distortions in test size and power caused by model misspecification, and demonstrate the advantages of nonparametric replication in such scenarios.

翻译：已有多种假设检验方法被提出，用于验证空间点模式的各向同性假设。这些方法大多具有一个共同特征：在原假设（各向同性）下，检验统计量的分布是未知的。参数化方法通过从用户指定的各向同性模型模拟点模式来近似该分布。另一种方案是使用各向同性条件下的非参数化复制统计量，从而避免指定模型的需要。本文首先构建了一个通用框架，允许将选定的非参数复制方法整合到各向同性检验中。随后，我们开展了一项包含多种类应用场景的大规模模拟研究，以评估采用不同参数与非参数复制方法的检验性能。特别地，我们探究了模型误设导致的检验尺度与功效扭曲，并论证了在此类场景中非参数复制方法的优势。