IDEAS home Printed from https://ideas.repec.org/a/bla/jorssc/v71y2022i1p244-268.html
   My bibliography  Save this article

Second‐order semi‐parametric inference for multivariate log Gaussian Cox processes

Author

Listed:
  • Kristian Bjørn Hessellund
  • Ganggang Xu
  • Yongtao Guan
  • Rasmus Waagepetersen

Abstract

This paper introduces a new approach to inferring the second‐order properties of a multivariate log Gaussian Cox process (LGCP) with a complex intensity function. We assume a semi‐parametric model for the multivariate intensity function containing an unspecified complex factor common to all types of points. Given this model, we construct a second‐order conditional composite likelihood to infer the pair correlation and cross pair correlation functions of the LGCP. Crucially this likelihood does not depend on the unspecified part of the intensity function. We also introduce a cross‐validation method for model selection and an algorithm for regularized inference that can be used to obtain sparse models for cross pair correlation functions. The methodology is applied to simulated data as well as data examples from microscopy and criminology. This shows how the new approach outperforms existing alternatives where the intensity functions are estimated non‐parametrically.

Suggested Citation

  • Kristian Bjørn Hessellund & Ganggang Xu & Yongtao Guan & Rasmus Waagepetersen, 2022. "Second‐order semi‐parametric inference for multivariate log Gaussian Cox processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(1), pages 244-268, January.
    • Handle: RePEc:bla:jorssc:v:71:y:2022:i:1:p:244-268
    DOI: 10.1111/rssc.12530
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/rssc.12530
    Download Restriction: no
    File URL: https://libkey.io/10.1111/rssc.12530?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. P. J. Diggle & V. Gómez-Rubio & P. E. Brown & A. G. Chetwynd & S. Gooding, 2007. "Second-Order Analysis of Inhomogeneous Spatial Point Processes Using Case–Control Data," Biometrics, The International Biometric Society, vol. 63(2), pages 550-557, June.
    2. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    3. Adrian Baddeley & Aruna Jammalamadaka & Gopalan Nair, 2014. "Multitype point process analysis of spines on the dendrite network of a neuron," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(5), pages 673-694, November.
    4. Yiyi Yan & Alexey A Leontovich & Michael J Gerdes & Keyur Desai & Jinhong Dong & Anup Sood & Alberto Santamaria-Pang & Aaron S Mansfield & Chrystal Chadwick & Rong Zhang & Wendy K Nevala & Thomas J Fl, 2019. "Understanding heterogeneous tumor microenvironment in metastatic melanoma," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-23, June.
    5. repec:bla:biomet:v:71:y:2015:i:4:p:1022-1033 is not listed on IDEAS
    6. Rasmus Waagepetersen & Yongtao Guan & Abdollah Jalilian & Jorge Mateu, 2016. "Analysis of multispecies point patterns by using multivariate log-Gaussian Cox processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(1), pages 77-96, January.
    7. Roy S. Herbst & Jean-Charles Soria & Marcin Kowanetz & Gregg D. Fine & Omid Hamid & Michael S. Gordon & Jeffery A. Sosman & David F. McDermott & John D. Powderly & Scott N. Gettinger & Holbrook E. K. , 2014. "Predictive correlates of response to the anti-PD-L1 antibody MPDL3280A in cancer patients," Nature, Nature, vol. 515(7528), pages 563-567, November.
    8. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    9. 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.
    10. Guan, Yongtao & Waagepetersen, Rasmus & Beale, Colin M., 2008. "Second-Order Analysis of Inhomogeneous Spatial Point Processes With Proportional Intensity Functions," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 769-777, June.
    11. T. Rajala & D. J. Murrell & S. C. Olhede, 2018. "Detecting multivariate interactions in spatial point patterns with Gibbs models and variable selection," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1237-1273, November.
    12. O Cronie & M N M Van Lieshout, 2018. "A non-model-based approach to bandwidth selection for kernel estimators of spatial intensity functions," Biometrika, Biometrika Trust, vol. 105(2), pages 455-462.
    Full references (including those not matched with items on IDEAS)

    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. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    2. Oxana Babecka Kucharcukova & Jan Bruha, 2016. "Nowcasting the Czech Trade Balance," Working Papers 2016/11, Czech National Bank.
    3. Carstensen, Kai & Heinrich, Markus & Reif, Magnus & Wolters, Maik H., 2020. "Predicting ordinary and severe recessions with a three-state Markov-switching dynamic factor model," International Journal of Forecasting, Elsevier, vol. 36(3), pages 829-850.
    4. Hou-Tai Chang & Ping-Huai Wang & Wei-Fang Chen & Chen-Ju Lin, 2022. "Risk Assessment of Early Lung Cancer with LDCT and Health Examinations," IJERPH, MDPI, vol. 19(8), pages 1-12, April.
    5. Margherita Giuzio, 2017. "Genetic algorithm versus classical methods in sparse index tracking," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 243-256, November.
    6. Nicolaj N. Mühlbach, 2020. "Tree-based Synthetic Control Methods: Consequences of moving the US Embassy," CREATES Research Papers 2020-04, Department of Economics and Business Economics, Aarhus University.
    7. Adam N. Smith & Stephan Seiler & Ishant Aggarwal, 2023. "Optimal Price Targeting," Marketing Science, INFORMS, vol. 42(3), pages 476-499, May.
    8. Wang, Qiao & Zhou, Wei & Cheng, Yonggang & Ma, Gang & Chang, Xiaolin & Miao, Yu & Chen, E, 2018. "Regularized moving least-square method and regularized improved interpolating moving least-square method with nonsingular moment matrices," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 120-145.
    9. Mert Demirer & Francis X. Diebold & Laura Liu & Kamil Yilmaz, 2018. "Estimating global bank network connectedness," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(1), pages 1-15, January.
    10. Wang, Tao & Zhu, Lixing, 2013. "Sparse sufficient dimension reduction using optimal scoring," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 223-232.
    11. Dmitriy Drusvyatskiy & Adrian S. Lewis, 2018. "Error Bounds, Quadratic Growth, and Linear Convergence of Proximal Methods," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 919-948, August.
    12. Mkhadri, Abdallah & Ouhourane, Mohamed, 2013. "An extended variable inclusion and shrinkage algorithm for correlated variables," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 631-644.
    13. Lucian Belascu & Alexandra Horobet & Georgiana Vrinceanu & Consuela Popescu, 2021. "Performance Dissimilarities in European Union Manufacturing: The Effect of Ownership and Technological Intensity," Sustainability, MDPI, vol. 13(18), pages 1-19, September.
    14. Marie Bessec, 2013. "Short‐Term Forecasts of French GDP: A Dynamic Factor Model with Targeted Predictors," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(6), pages 500-511, September.
    15. Candelon, B. & Hurlin, C. & Tokpavi, S., 2012. "Sampling error and double shrinkage estimation of minimum variance portfolios," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 511-527.
    16. Ardyn Nordstrom, 2021. "Can Interventions Targeting Community Attitudes Improve Education for Marginalized Students? Evidence from a Mixed-Methods Experimental Design in Zimbabwe," Working Paper 1472, Economics Department, Queen's University.
    17. Susan Athey & Guido W. Imbens & Stefan Wager, 2018. "Approximate residual balancing: debiased inference of average treatment effects in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 597-623, September.
    18. Diego Vidaurre & Concha Bielza & Pedro Larrañaga, 2013. "A Survey of L1 Regression," International Statistical Review, International Statistical Institute, vol. 81(3), pages 361-387, December.
    19. Luis Fernando Melo-Velandia & Juan J. Ospina-Tejeiro & Julian A. Parra-Polania, 2020. "Effects of Banco de la Republica’s Communication on the Yield Curve," Borradores de Economia 1137, Banco de la Republica de Colombia.
    20. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2025. "Specification Choices in Quantile Regression for Empirical Macroeconomics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 40(1), pages 57-73, January.

    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:jorssc:v:71:y:2022:i:1:p:244-268. 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.