We analyze data occurring in a regular two-dimensional grid for spatial dependence based on spatial ordinal patterns (SOPs). After having derived the asymptotic distribution of the SOP frequencies under the null hypothesis of spatial independence, we use the concept of the type of SOPs to define the statistics to test for spatial dependence. The proposed tests are not only implemented for real-valued random variables, but a solution for discrete-valued spatial processes in the plane is provided as well. The performances of the spatial-dependence tests are comprehensively analyzed by simulations, considering various data-generating processes. The results show that SOP-based dependence tests have good size properties and constitute an important and valuable complement to the spatial autocorrelation function. To be more specific, SOP-based tests can detect spatial dependence in non-linear processes, and they are robust with respect to outliers and zero inflation. To illustrate their application in practice, two real-world data examples from agricultural sciences are analyzed.

我们根据空间序数模式 (SOP) 分析规则二维网格中的数据的空间依赖性。在空间独立性原假设下导出 SOP 频率的渐近分布后，我们使用 SOP 类型的概念来定义统计量以测试空间依赖性。所提出的测试不仅适用于实值随机变量，而且还提供了平面上离散值空间过程的解决方案。考虑各种数据生成过程，通过模拟全面分析空间依赖性测试的性能。结果表明，基于 SOP 的相关性检验具有良好的尺寸特性，是对空间自相关函数的重要且有价值的补充。更具体地说，基于 SOP 的测试可以检测非线性过程中的空间依赖性，并且它们对于异常值和零膨胀具有鲁棒性。为了说明其在实践中的应用，分析了农业科学中的两个现实世界数据示例。