IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v71y2009i3p685-702.html
   My bibliography  Save this article

Two‐step estimation for inhomogeneous spatial point processes

Author

Listed:
  • Rasmus Waagepetersen
  • Yongtao Guan

Abstract

Summary. The paper is concerned with parameter estimation for inhomogeneous spatial point processes with a regression model for the intensity function and tractable second‐order properties (K‐function). Regression parameters are estimated by using a Poisson likelihood score estimating function and in the second step minimum contrast estimation is applied for the residual clustering parameters. Asymptotic normality of parameter estimates is established under certain mixing conditions and we exemplify how the results may be applied in ecological studies of rainforests.

Suggested Citation

  • Rasmus Waagepetersen & Yongtao Guan, 2009. "Two‐step estimation for inhomogeneous spatial point processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 685-702, June.
    • Handle: RePEc:bla:jorssb:v:71:y:2009:i:3:p:685-702
    DOI: 10.1111/j.1467-9868.2008.00702.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9868.2008.00702.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9868.2008.00702.x?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
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. A. J. Baddeley & J. Møller & R. Waagepetersen, 2000. "Non‐ and semi‐parametric estimation of interaction in inhomogeneous point patterns," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(3), pages 329-350, November.
    3. 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.
    4. Yongtao Guan & Michael Sherman, 2007. "On least squares fitting for stationary spatial point processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 31-49, February.
    5. Waagepetersen, Rasmus, 2004. "Convergence of posteriors for discretized log Gaussian Cox processes," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 229-235, February.
    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. Maciak, Matúš & Okhrin, Ostap & Pešta, Michal, 2021. "Infinitely stochastic micro reserving," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 30-58.
    2. Michaela Prokešová & Jiří Dvořák, 2014. "Statistics for Inhomogeneous Space-Time Shot-Noise Cox Processes," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 433-449, June.
    3. Qing-Song Yang & Guo-Chun Shen & He-Ming Liu & Zhang-Hua Wang & Zun-Ping Ma & Xiao-Feng Fang & Jian Zhang & Xi-Hua Wang, 2016. "Detangling the Effects of Environmental Filtering and Dispersal Limitation on Aggregated Distributions of Tree and Shrub Species: Life Stage Matters," PLOS ONE, Public Library of Science, vol. 11(5), pages 1-16, May.
    4. Nicoletta D’Angelo & Marianna Siino & Antonino D’Alessandro & Giada Adelfio, 2022. "Local spatial log-Gaussian Cox processes for seismic data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 633-671, December.
    5. Yu Ryan Yue & Ji Meng Loh, 2011. "Bayesian Semiparametric Intensity Estimation for Inhomogeneous Spatial Point Processes," Biometrics, The International Biometric Society, vol. 67(3), pages 937-946, September.
    6. Abdollah Jalilian, 2017. "Modelling and classification of species abundance: a case study in the Barro Colorado Island plot," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2401-2409, October.
    7. Jalilian, Abdollah, 2016. "On the higher order product density functions of a Neyman–Scott cluster point process," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 144-150.
    8. Jean-François Coeurjolly, 2017. "Median-based estimation of the intensity of a spatial point process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 303-331, April.
    9. Chong Deng & Yongtao Guan & Rasmus P. Waagepetersen & Jingfei Zhang, 2017. "Second‐order quasi‐likelihood for spatial point processes," Biometrics, The International Biometric Society, vol. 73(4), pages 1311-1320, December.
    10. Federico Ferraccioli & Eleonora Arnone & Livio Finos & James O. Ramsay & Laura M. Sangalli, 2021. "Nonparametric density estimation over complicated domains," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(2), pages 346-368, April.
    11. T. Mrkvička, 2014. "Distinguishing Different Types of Inhomogeneity in Neyman–Scott Point Processes," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 385-395, June.
    12. Xinyu Zhou & Wei Wu, 2024. "Statistical Depth in Spatial Point Process," Mathematics, MDPI, vol. 12(4), pages 1-20, February.
    13. María P. Frías & Antoni Torres-Signes & María D. Ruiz-Medina & Jorge Mateu, 2022. "Spatial Cox processes in an infinite-dimensional framework," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 175-203, March.
    14. Ute Hahn & Eva B. Vedel Jensen, 2016. "Hidden Second-order Stationary Spatial Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 455-475, June.
    15. Biscio, Christophe Ange Napoléon & Poinas, Arnaud & Waagepetersen, Rasmus, 2018. "A note on gaps in proofs of central limit theorems," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 7-10.
    16. Michaela Prokešová & Jiří Dvořák & Eva B. Vedel Jensen, 2017. "Two-step estimation procedures for inhomogeneous shot-noise Cox processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(3), pages 513-542, June.
    17. Jean-François Coeurjolly & Jesper Møller & Rasmus Waagepetersen, 2017. "A Tutorial on Palm Distributions for Spatial Point Processes," International Statistical Review, International Statistical Institute, vol. 85(3), pages 404-420, December.
    18. Christophe Ange Napoléon Biscio & Frédéric Lavancier, 2017. "Contrast Estimation for Parametric Stationary Determinantal Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 204-229, March.
    19. Tilman M. Davies & Martin L. Hazelton, 2013. "Assessing minimum contrast parameter estimation for spatial and spatiotemporal log‐Gaussian Cox processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 355-389, November.
    20. Jiří Dvořák & Michaela Prokešová, 2016. "Parameter Estimation for Inhomogeneous Space-Time Shot-Noise Cox Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 939-961, December.
    21. Poinas, Arnaud, 2019. "A bound of the β-mixing coefficient for point processes in terms of their intensity functions," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 88-93.
    22. Shengde Liang & Sudipto Banerjee & Bradley P. Carlin, 2009. "Bayesian Wombling for Spatial Point Processes," Biometrics, The International Biometric Society, vol. 65(4), pages 1243-1253, December.
    23. Mat'uv{s} Maciak & Ostap Okhrin & Michal Pev{s}ta, 2019. "Infinitely Stochastic Micro Forecasting," Papers 1908.10636, arXiv.org, revised Sep 2019.

    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. Michaela Prokešová & Jiří Dvořák & Eva B. Vedel Jensen, 2017. "Two-step estimation procedures for inhomogeneous shot-noise Cox processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(3), pages 513-542, June.
    2. Yongtao Guan, 2008. "Variance estimation for statistics computed from inhomogeneous spatial point processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 175-190, February.
    3. Jesper Møller & Carlos Díaz‐Avalos, 2010. "Structured Spatio‐Temporal Shot‐Noise Cox Point Process Models, with a View to Modelling Forest Fires," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(1), pages 2-25, March.
    4. Yu Ryan Yue & Ji Meng Loh, 2011. "Bayesian Semiparametric Intensity Estimation for Inhomogeneous Spatial Point Processes," Biometrics, The International Biometric Society, vol. 67(3), pages 937-946, September.
    5. P. A. Henrys & P. E. Brown, 2009. "Inference for Clustered Inhomogeneous Spatial Point Processes," Biometrics, The International Biometric Society, vol. 65(2), pages 423-430, June.
    6. Ute Hahn & Eva B. Vedel Jensen, 2016. "Hidden Second-order Stationary Spatial Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 455-475, June.
    7. Tilman M. Davies & Martin L. Hazelton, 2013. "Assessing minimum contrast parameter estimation for spatial and spatiotemporal log‐Gaussian Cox processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 355-389, November.
    8. Yongtao Guan & Hansheng Wang, 2010. "Sufficient dimension reduction for spatial point processes directed by Gaussian random fields," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 367-387, June.
    9. 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.
    10. Jesper Møller & Heidi S. Christensen & Francisco Cuevas-Pacheco & Andreas D. Christoffersen, 2021. "Structured Space-Sphere Point Processes and K-Functions," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 569-591, June.
    11. Frédéric Lavancier & Arnaud Poinas & Rasmus Waagepetersen, 2021. "Adaptive estimating function inference for nonstationary determinantal point processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 87-107, March.
    12. Nicoletta D’Angelo & Marianna Siino & Antonino D’Alessandro & Giada Adelfio, 2022. "Local spatial log-Gaussian Cox processes for seismic data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 633-671, December.
    13. Jalilian, Abdollah, 2016. "On the higher order product density functions of a Neyman–Scott cluster point process," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 144-150.
    14. Yehua Li & Yongtao Guan, 2014. "Functional Principal Component Analysis of Spatiotemporal Point Processes With Applications in Disease Surveillance," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1205-1215, September.
    15. Deng, C. & Waagepetersen, R.P. & Wang, M. & Guan, Y., 2018. "A fast spectral quasi-likelihood approach for spatial point processes," Statistics & Probability Letters, Elsevier, vol. 133(C), pages 59-64.
    16. Biscio, Christophe Ange Napoléon & Poinas, Arnaud & Waagepetersen, Rasmus, 2018. "A note on gaps in proofs of central limit theorems," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 7-10.
    17. Zhang, Tonglin & Mateu, Jorge, 2019. "Substationarity for spatial point processes," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 22-36.
    18. Isabel Fuentes-Santos & Wenceslao González-Manteiga & Jorge Mateu, 2016. "Consistent Smooth Bootstrap Kernel Intensity Estimation for Inhomogeneous Spatial Poisson Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 416-435, June.
    19. Borrajo, M.I. & González-Manteiga, W. & Martínez-Miranda, M.D., 2024. "Goodness-of-fit test for point processes first-order intensity," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).
    20. T. Mrkvička, 2014. "Distinguishing Different Types of Inhomogeneity in Neyman–Scott Point Processes," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 385-395, June.

    More about this item

    Statistics

    Access and download statistics

    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:bla:jorssb:v:71:y:2009:i:3:p:685-702. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    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.