Nonparametric testing of the dependence structure among points-marks-covariates in spatial point patterns
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We investigate the problem of testing the hypothesis of independence between a covariate and the marks in a marked point process. This would be rather straightforward if the (unmarked) process of points was independent of the covariate and the marks. In practice, however, such an assumption is questionable, and possible preferential sampling effects (dependence between the point process and the covariate and/or the marks) may lead to incorrect conclusions. Hence 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 also 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.
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