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

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  • Jiří Dvořák
  • Tomáš Mrkvička
  • Jorge Mateu
  • Jonatan A. González

Abstract

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.

Suggested Citation

  • Jiří Dvořák & Tomáš Mrkvička & Jorge Mateu & Jonatan A. González, 2022. "Nonparametric Testing of the Dependence Structure Among Points–Marks–Covariates in Spatial Point Patterns," International Statistical Review, International Statistical Institute, vol. 90(3), pages 592-621, December.
  • Handle: RePEc:bla:istatr:v:90:y:2022:i:3:p:592-621
    DOI: 10.1111/insr.12503
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    References listed on IDEAS

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    4. Grabarnik, Pavel & Myllymäki, Mari & Stoyan, Dietrich, 2011. "Correct testing of mark independence for marked point patterns," Ecological Modelling, Elsevier, vol. 222(23), pages 3888-3894.
    5. Freedman, David & Lane, David, 1983. "A Nonstochastic Interpretation of Reported Significance Levels," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(4), pages 292-298, October.
    6. Mark Berman, 1986. "Testing for Spatial Association between a Point Process and Another Stochastic Process," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 35(1), pages 54-62, March.
    7. Martin Schlather & Paulo J. Ribeiro & Peter J. Diggle, 2004. "Detecting dependence between marks and locations of marked point processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 79-93, February.
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