IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v155y2017icp72-82.html
   My bibliography  Save this article

Testing proportionality between the first-order intensity functions of spatial point processes

Author

Listed:
  • Zhang, Tonglin
  • Zhuang, Run

Abstract

This article proposes a Kolmogorov–Smirnov type test for proportionality between the first-order intensity functions of two independent spatial point processes. After appropriate scaling, the test statistic is constructed by maximizing the absolute difference between their point densities over a π-system. By treating non-stationary point processes as transformed from stationary point processes such that all questions of asymptotics related to the tightness can be answered, the article shows that the resulting test statistic converges weakly to the absolute maximum of a pinned Brownian sheet. This may be reduced to the standard Brownian bridge in a special case. A simulation study shows that the type I error probability of the test is close to the significance level and the power function increases to 1 as the magnitude of non-proportionality increases. In applications to two typical natural hazard data, the article concludes that the first-order intensity functions might be proportional in one case and not in the other.

Suggested Citation

  • Zhang, Tonglin & Zhuang, Run, 2017. "Testing proportionality between the first-order intensity functions of spatial point processes," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 72-82.
    • Handle: RePEc:eee:jmvana:v:155:y:2017:i:c:p:72-82
    DOI: 10.1016/j.jmva.2016.11.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X16301968
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2016.11.013?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yongtao Guan & Michael Sherman & James A. Calvin, 2006. "Assessing Isotropy for Spatial Point Processes," Biometrics, The International Biometric Society, vol. 62(1), pages 119-125, March.
    2. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
    3. Peter Diggle & Pingping Zheng & Peter Durr, 2005. "Nonparametric estimation of spatial segregation in a multivariate point process: bovine tuberculosis in Cornwall, UK," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 645-658, June.
    4. Frederic Paik Schoenberg, 2004. "Testing Separability in Spatial-Temporal Marked Point Processes," Biometrics, The International Biometric Society, vol. 60(2), pages 471-481, June.
    5. Yongtao Guan, 2008. "A KPSS Test for Stationarity for Spatial Point Processes," Biometrics, The International Biometric Society, vol. 64(3), pages 800-806, September.
    6. Ivanoff, Gail, 1982. "Central limit theorems for point processes," Stochastic Processes and their Applications, Elsevier, vol. 12(2), pages 171-186, March.
    7. Roger D. Peng & Frederic Paik Schoenberg & James A. Woods, 2005. "A Space-Time Conditional Intensity Model for Evaluating a Wildfire Hazard Index," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 26-35, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhang, Tonglin & Mateu, Jorge, 2019. "Substationarity for spatial point processes," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 22-36.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sebastian Meyer & Johannes Elias & Michael Höhle, 2012. "A Space–Time Conditional Intensity Model for Invasive Meningococcal Disease Occurrence," Biometrics, The International Biometric Society, vol. 68(2), pages 607-616, June.
    2. Markéta Zikmundová & Kateřina Staňková Helisová & Viktor Beneš, 2012. "Spatio-Temporal Model for a Random Set Given by a Union of Interacting Discs," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 883-894, September.
    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.
    4. Rakhee Dinubhai Patel & Frederic Paik Schoenberg, 2011. "A graphical test for local self-similarity in univariate data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2547-2562, January.
    5. Xinyu Zhou & Wei Wu, 2024. "Statistical Depth in Spatial Point Process," Mathematics, MDPI, vol. 12(4), pages 1-20, February.
    6. Zhang, Tonglin & Mateu, Jorge, 2019. "Substationarity for spatial point processes," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 22-36.
    7. Alexandre Rodrigues & Peter Diggle & Renato Assuncao, 2010. "Semiparametric approach to point source modelling in epidemiology and criminology," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(3), pages 533-542, May.
    8. Dewei Wang & Chendi Jiang & Chanseok Park, 2019. "Reliability analysis of load-sharing systems with memory," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(2), pages 341-360, April.
    9. Jamie Olson & Kathleen Carley, 2013. "Exact and approximate EM estimation of mutually exciting hawkes processes," Statistical Inference for Stochastic Processes, Springer, vol. 16(1), pages 63-80, April.
    10. Heinrich Lothar & Klein Stella, 2011. "Central limit theorem for the integrated squared error of the empirical second-order product density and goodness-of-fit tests for stationary point processes," Statistics & Risk Modeling, De Gruyter, vol. 28(4), pages 359-387, December.
    11. van den Hengel, G. & Franses, Ph.H.B.F., 2018. "Forecasting social conflicts in Africa using an Epidemic Type Aftershock Sequence model," Econometric Institute Research Papers EI2018-31, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    12. Chenlong Li & Zhanjie Song & Wenjun Wang, 2020. "Space–time inhomogeneous background intensity estimators for semi-parametric space–time self-exciting point process models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 945-967, August.
    13. Lizhen Xu & Jason A. Duan & Andrew Whinston, 2014. "Path to Purchase: A Mutually Exciting Point Process Model for Online Advertising and Conversion," Management Science, INFORMS, vol. 60(6), pages 1392-1412, June.
    14. Møller, Jesper & Torrisi, Giovanni Luca, 2007. "The pair correlation function of spatial Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 995-1003, June.
    15. Giada Adelfio & Arianna Agosto & Marcello Chiodi & Paolo Giudici, 2021. "Financial contagion through space-time point processes," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 665-688, June.
    16. Fama, Yuchen & Pozdnyakov, Vladimir, 2011. "A test for self-exciting clustering mechanism," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1541-1546, October.
    17. Francine Gresnigt & Erik Kole & Philip Hans Franses, 2017. "Exploiting Spillovers to Forecast Crashes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(8), pages 936-955, December.
    18. Jiménez, Abigail, 2011. "Comparison of the Hurst and DEA exponents between the catalogue and its clusters: The California case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 2146-2154.
    19. Sobin Joseph & Shashi Jain, 2024. "Non-Parametric Estimation of Multi-dimensional Marked Hawkes Processes," Papers 2402.04740, arXiv.org.
    20. Martin Magris, 2019. "On the simulation of the Hawkes process via Lambert-W functions," Papers 1907.09162, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:155:y:2017:i:c:p:72-82. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.