Nonparametric testing of the dependence structure among points-marks-covariates in spatial point patterns

Abstract

We investigate testing of the hypothesis of independence between a covariate and the marks in amarked point process. It would be rather straightforward if the (unmarked) point process wereindependent of the covariate and the marks. In practice, however, such an assumption isquestionable and possible dependence between the point process and the covariate or the marksmay lead to incorrect conclusions. Therefore, we propose to investigate the complete dependencestructure in the triangle points–marks–covariates together. We take advantage of the recentdevelopment of the nonparametric random shift methods, namely, the new variance correctionapproach, and propose tests of the null hypothesis of independence between the marks and thecovariate and between the points and the covariate. We present a detailed simulation study showingthe performance of the methods and provide two theorems establishing the appropriate form of thecorrection factors for the variance correction. Finally, we illustrate the use of the proposed methodsin two real applications.