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Poles of pair correlation functions: When they are real?

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  • Ka Yiu Wong

    (Technische Universität Bergakademie Freiberg)

  • Dietrich Stoyan

    (Technische Universität Bergakademie Freiberg)

Abstract

The most common standard estimator of the pair correlation function (PCF) of a point process has a pole at zero, which is in most cases a statistical artifact. However, sometimes it makes sense to assume that a pole really exists. We propose two independent approaches for the proof of existence of a PCF’s pole and for the determination of its order. In the first, we use a summary characteristic F that transforms the PCF’s pole order to the location of F’s pole, while the other one uses a natural estimation method based on Ripley’s K-function. These methods are applied to simulated samples of two classical point process models and two cluster point process models with special geometries. Finally, we use the approach in the statistical analysis of a classical point pattern of pine trees and a highly clustered pattern of nonmetallic inclusions in steel.

Suggested Citation

  • Ka Yiu Wong & Dietrich Stoyan, 2021. "Poles of pair correlation functions: When they are real?," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(2), pages 425-440, April.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:2:d:10.1007_s10463-020-00754-3
    DOI: 10.1007/s10463-020-00754-3
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    References listed on IDEAS

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    1. Mohammad Ghorbani, 2013. "Cauchy cluster process," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(5), pages 697-706, July.
    2. Sung Nok Chiu & Kwong Ip Liu, 2013. "Stationarity Tests for Spatial Point Processes using Discrepancies," Biometrics, The International Biometric Society, vol. 69(2), pages 497-507, June.
    3. Yongtao Guan, 2008. "A KPSS Test for Stationarity for Spatial Point Processes," Biometrics, The International Biometric Society, vol. 64(3), pages 800-806, September.
    4. Guan, Yongtao, 2007. "A least-squares cross-validation bandwidth selection approach in pair correlation function estimations," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1722-1729, December.
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    Cited by:

    1. Jonatan A. González & Francisco J. Rodríguez-Cortés & Elvira Romano & Jorge Mateu, 2021. "Classification of Events Using Local Pair Correlation Functions for Spatial Point Patterns," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(4), pages 538-559, December.

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