IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v22y2020i3d10.1007_s11009-019-09749-x.html
   My bibliography  Save this article

Infill Asymptotics and Bandwidth Selection for Kernel Estimators of Spatial Intensity Functions

Author

Listed:
  • M. N. M. Lieshout

    (CWI
    University of Twente)

Abstract

We investigate the asymptotic mean squared error of kernel estimators of the intensity function of a spatial point process. We derive expansions for the bias and variance in the scenario that n independent copies of a point process in ℝ d $\mathbb {R}^{d}$ are superposed. When the same bandwidth is used in all d dimensions, we show that an optimal bandwidth exists and is of the order n− 1/(d+ 4) under appropriate smoothness conditions on the true intensity function.

Suggested Citation

  • M. N. M. Lieshout, 2020. "Infill Asymptotics and Bandwidth Selection for Kernel Estimators of Spatial Intensity Functions," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 995-1008, September.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:3:d:10.1007_s11009-019-09749-x
    DOI: 10.1007/s11009-019-09749-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-019-09749-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-019-09749-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
    ---><---

    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. 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.
    2. 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.
    3. V. Granville, 1998. "Estimation of the intensity of a Poisson point process by means of nearest neighbor distances," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(1), pages 112-124, March.
    4. Marie-Colette N. M. Lieshout, 2012. "On Estimation of the Intensity Function of a Point Process," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 567-578, September.
    5. Peter Diggle, 1985. "A Kernel Method for Smoothing Point Process Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(2), pages 138-147, June.
    6. Brooks, Maria Mori & Marron, J. Stephen, 1991. "Asymptotic optimality of the least-squares cross-validation bandwidth for kernel estimates of intensity functions," Stochastic Processes and their Applications, Elsevier, vol. 38(1), pages 157-165, June.
    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. Borrajo, M.I. & González-Manteiga, W. & Martínez-Miranda, M.D., 2020. "Bootstrapping kernel intensity estimation for inhomogeneous point processes with spatial covariates," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    2. Camerlenghi, F. & Capasso, V. & Villa, E., 2014. "On the estimation of the mean density of random closed sets," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 65-88.
    3. Marie-Colette N. M. Lieshout, 2012. "On Estimation of the Intensity Function of a Point Process," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 567-578, September.
    4. 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.
    5. Amaya-Gómez, Rafael & Sánchez-Silva, Mauricio & Muñoz, Felipe & Schoefs, Franck & Bastidas-Arteaga, Emilio, 2024. "Spatial characterization and simulation of new defects in corroded pipeline based on In-Line Inspections," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    6. Giuseppe Espa & Giuseppe Arbia & Diego Giuliani, 2013. "Conditional versus unconditional industrial agglomeration: disentangling spatial dependence and spatial heterogeneity in the analysis of ICT firms’ distribution in Milan," Journal of Geographical Systems, Springer, vol. 15(1), pages 31-50, January.
    7. Mola-Yudego, Blas & Selkimäki, Mari & González-Olabarria, José Ramón, 2014. "Spatial analysis of the wood pellet production for energy in Europe," Renewable Energy, Elsevier, vol. 63(C), pages 76-83.
    8. Yingqi Zhao & Donglin Zeng & Amy H. Herring & Amy Ising & Anna Waller & David Richardson & Michael R. Kosorok, 2011. "Detecting Disease Outbreaks Using Local Spatiotemporal Methods," Biometrics, The International Biometric Society, vol. 67(4), pages 1508-1517, December.
    9. François Sémécurbe & Cécile Tannier & Stéphane G. Roux, 2019. "Applying two fractal methods to characterise the local and global deviations from scale invariance of built patterns throughout mainland France," Journal of Geographical Systems, Springer, vol. 21(2), pages 271-293, June.
    10. Peng Hou & Xiaojian Yi & Haiping Dong, 2020. "A Spatial Statistic Based Risk Assessment Approach to Prioritize the Pipeline Inspection of the Pipeline Network," Energies, MDPI, vol. 13(3), pages 1-16, February.
    11. 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.
    12. Ondřej Šedivý & Antti Penttinen, 2014. "Intensity estimation for inhomogeneous Gibbs point process with covariates-dependent chemical activity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(3), pages 225-249, August.
    13. Bouezmarni, Taoufik & Rombouts, Jeroen V.K., 2010. "Nonparametric density estimation for positive time series," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 245-261, February.
    14. Marcon, Eric & Puech, Florence, 2017. "A typology of distance-based measures of spatial concentration," Regional Science and Urban Economics, Elsevier, vol. 62(C), pages 56-67.
    15. Wenyang Zhang & Qiwei Yao & Howell Tong & Nils Chr. Stenseth, 2003. "Smoothing for Spatiotemporal Models and Its Application to Modeling Muskrat-Mink Interaction," Biometrics, The International Biometric Society, vol. 59(4), pages 813-821, December.
    16. Afshartous, David & Guan, Yongtao & Mehrotra, Anuj, 2009. "US Coast Guard air station location with respect to distress calls: A spatial statistics and optimization based methodology," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1086-1096, August.
    17. Federico Camerlenghi & Claudio Macci & Elena Villa, 2021. "Asymptotic behavior of mean density estimators based on a single observation: the Boolean model case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 1011-1035, October.
    18. Andrea Cerioli & Domenico Perrotta, 2014. "Robust clustering around regression lines with high density regions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(1), pages 5-26, March.
    19. Julia A. Palacios & Vladimir N. Minin, 2013. "Gaussian Process-Based Bayesian Nonparametric Inference of Population Size Trajectories from Gene Genealogies," Biometrics, The International Biometric Society, vol. 69(1), pages 8-18, March.
    20. María Cristina Rodríguez Rangel & Marcelino Sánchez Rivero & Julián Ramajo Hernández, 2020. "A Spatial Analysis of Intensity in Tourism Accommodation: An Application for Extremadura (Spain)," Economies, MDPI, vol. 8(2), pages 1-21, April.

    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:spr:metcap:v:22:y:2020:i:3:d:10.1007_s11009-019-09749-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.