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Empirical Mark Covariance and Product Density Function of Stationary Marked Point Processes—A Survey on Asymptotic Results

Author

Listed:
  • Lothar Heinrich

    (Augsburg University)

  • Stella Klein

    (Augsburg University)

  • Martin Moser

    (Munich University of Technology)

Abstract

Marked point processes are stochastic models to describe random patterns of marked points {[X i ,M i ], i ≥ 1} in some bounded subset of the d-dimensional Euclidean space (usually d = 1, 2 or 3 in applications), where each point X i carries additional random information expressed as mark M i taking values in some metric space. To study the correlations between distinct points and between marks located at distinct points we use kernel-type estimators of the second-order product density and the mark covariance function of a spatially homogeneous marked point process. Both functions and their empirical counterparts are suitable characteristics to identify point process models by construction of statistical goodness-of-fit tests.

Suggested Citation

  • Lothar Heinrich & Stella Klein & Martin Moser, 2014. "Empirical Mark Covariance and Product Density Function of Stationary Marked Point Processes—A Survey on Asymptotic Results," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 283-293, June.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:2:d:10.1007_s11009-012-9314-7
    DOI: 10.1007/s11009-012-9314-7
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