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A concentration inequality for inhomogeneous Neyman–Scott point processes

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  • Coeurjolly, Jean-François
  • Reynaud-Bouret, Patricia

Abstract

In this note, we prove some non-asymptotic concentration inequalities for functionals, called innovations, of inhomogeneous Neyman–Scott point processes, a particular class of spatial point process models. Innovation is a functional built from the counting measure minus its integral compensator. The result is then applied to obtain almost sure rate of convergence for such functionals.

Suggested Citation

  • Coeurjolly, Jean-François & Reynaud-Bouret, Patricia, 2019. "A concentration inequality for inhomogeneous Neyman–Scott point processes," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 30-34.
    • Handle: RePEc:eee:stapro:v:148:y:2019:i:c:p:30-34
    DOI: 10.1016/j.spl.2018.12.003
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    References listed on IDEAS

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    1. Coeurjolly, Jean-François, 2015. "Almost sure behavior of functionals of stationary Gibbs point processes," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 241-246.
    2. A. Baddeley & R. Turner & J. Møller & M. Hazelton, 2005. "Residual analysis for spatial point processes (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 617-666, November.
    3. Guan, Yongtao & Loh, Ji Meng, 2007. "A Thinned Block Bootstrap Variance Estimation Procedure for Inhomogeneous Spatial Point Patterns," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1377-1386, December.
    4. Rasmus Plenge Waagepetersen, 2007. "An Estimating Function Approach to Inference for Inhomogeneous Neyman–Scott Processes," Biometrics, The International Biometric Society, vol. 63(1), pages 252-258, March.
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