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Empirical distributions in marked point processes

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  • Pawlas, Zbynek

Abstract

We study the asymptotic behaviour of the empirical distribution function derived from a stationary marked point process when a convex sampling window is expanding without bounds in all directions. We consider a random field model which assumes that the marks and the points are independent and admits dependencies between the marks. The main result is the weak convergence of the empirical process under strong mixing conditions on both independent components of the model. Applying an approximation principle weak convergence can be also shown for appropriately weighted empirical process defined from a stationary d-dimensional germ-grain process with dependent grains.

Suggested Citation

  • Pawlas, Zbynek, 2009. "Empirical distributions in marked point processes," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4194-4209, December.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:12:p:4194-4209
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
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    Cited by:

    1. Jakub Staněk & Ondřej Šedivý & Viktor Beneš, 2014. "On Random Marked Sets with a Smaller Integer Dimension," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 397-410, June.
    2. 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.
    3. Dalderop, Jeroen, 2020. "Nonparametric filtering of conditional state-price densities," Journal of Econometrics, Elsevier, vol. 214(2), pages 295-325.

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