Nonparametric Testing of the Dependence Structure Among Points–Marks–Covariates in Spatial Point Patterns

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