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}
}
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… 
Gaussian limits of empirical multiparameter K-functions of homogeneous Poisson processes and tests for complete spatial randomness
We prove two functional limit theorems for empirical multiparameter second moment functions (generalizing Ripley’s K-function) obtained from a homogeneous Poisson point field observed in an

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