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

Jiří Dvořák*, Tomáš Mrkvička, Jorge Mateu, Jonatan A. González

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)592-621
Number of pages30
JournalInternational Statistical Review
Issue number3
StatePublished - Dec 2022

Bibliographical note

Funding Information:
This work was supported by Grant Agency of the Czech Republic (Project No. 19‐04412S). J. Mateu and J. A. González were partially supported by grants Ministerio de Ciencia e Innovación (MTM2016‐78917‐R), Generalitat Valenciana (AICO/2019/198) and Universitat Jaume I (UJI‐B2018‐04).

Publisher Copyright:
© 2022 International Statistical Institute.


  • Covariate
  • hypothesis testing
  • independence
  • marked point process
  • nonparametric inference

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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