We investigate testing of the hypothesis of independence between a covariate and the marks in a marked point process. It would be rather straightforward if the (unmarked) point process were independent of the covariate and the marks. In practice, however, such an assumption is questionable and possible dependence between the point process and the covariate or the marks may lead to incorrect conclusions. Therefore, we propose to investigate the complete dependence structure in the triangle points–marks–covariates together. We take advantage of the recent development of the nonparametric random shift methods, namely, the new variance correction approach, and propose tests of the null hypothesis of independence between the marks and the covariate and between the points and the covariate. We present a detailed simulation study showing the performance of the methods and provide two theorems establishing the appropriate form of the correction factors for the variance correction. Finally, we illustrate the use of the proposed methods in two real applications.

中文翻译：

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空间点模式中点-标记-协变量之间依赖结构的非参数检验

我们研究了在标记点过程中对协变量和标记之间独立性假设的检验。如果（未标记的）点过程独立于协变量和标记，那将是相当简单的。然而，在实践中，这样的假设是有问题的，并且点过程和协变量或标记之间的可能依赖关系可能会导致错误的结论。因此，我们建议一起研究三角形点-标记-协变量中的完全依赖结构。我们利用最近发展的非参数随机移位方法，即新的方差校正方法，提出了对标记与协变量之间以及点与协变量之间独立性的原假设的检验。我们提出了一个详细的模拟研究，展示了这些方法的性能，并提供了两个定理，建立了用于方差校正的校正因子的适当形式。最后，我们说明了所提出的方法在两个实际应用中的使用。