• DOI:10.1080/02331888.2018.1460367
• Corpus ID: 88515465

Asymptotic goodness-of-fit tests for point processes based on scaled empirical K-functions

@article{Heinrich2017AsymptoticGT,
  title={Asymptotic goodness-of-fit tests for point processes based on scaled empirical K-functions},
  author={L. Heinrich},
  journal={Statistics},
  year={2017},
  volume={52},
  pages={829 - 851}
}

• L. Heinrich
• Published 4 June 2017
• Mathematics
• Statistics

ABSTRACT We study sequences of scaled edge-corrected empirical (generalized) K-functions (modifying Ripley's K-function) each of them constructed from a single observation of a d-dimensional fourth-order stationary point process in a sampling window which grows together with some scaling rate unboundedly as . Under some natural assumptions it is shown that the normalized difference between scaled empirical and scaled theoretical K-function converges weakly to a mean zero Gaussian process with simple covariance function. This result suggests discrepancy measures between empirical and theoretical K-function with known limit distribution which allow to perform goodness-of-fit tests for checking a hypothesized point process based only on its intensity and (generalized) K-function. Similar test statistics are derived for testing the hypothesis that two independent point processes in have the same distribution without explicit knowledge of their intensities and K-functions.