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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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    1. S. Eckel & F. Fleischer & P. Grabarnik & V. Schmidt, 2008. "An investigation of the spatial correlations for relative purchasing power in Baden–Württemberg," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(2), pages 135-152, May.
    2. Yongtao Guan, 2006. "Tests for Independence between Marks and Points of a Marked Point Process," Biometrics, The International Biometric Society, vol. 62(1), pages 126-134, March.
    3. Pawlas, Zbynek, 2009. "Empirical distributions in marked point processes," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4194-4209, December.
    4. Shigeru Mase, 1996. "The threshold method for estimating total rainfall," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(2), pages 201-213, June.
    5. 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.
    6. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
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