IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v73y2021i5d10.1007_s10463-020-00775-y.html
   My bibliography  Save this article

Asymptotic behavior of mean density estimators based on a single observation: the Boolean model case

Author

Listed:
  • Federico Camerlenghi

    (Università di Milano - Bicocca
    Collegio Carlo Alberto
    Bocconi University)

  • Claudio Macci

    (Università di Roma Tor Vergata)

  • Elena Villa

    (Università degli Studi di Milano)

Abstract

The mean density estimation of a random closed set in $$\mathbb {R}^d$$ R d , based on a single observation, is a crucial problem in several application areas. In the case of stationary random sets, a common practice to estimate the mean density is to take the n-dimensional volume fraction with observation window as large as possible. In the present paper, we provide large and moderate deviation results for these estimators when the random closed set $$\Theta _n$$ Θ n belongs to the quite general class of stationary Boolean models with Hausdorff dimension $$n

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:5:d:10.1007_s10463-020-00775-y
    DOI: 10.1007/s10463-020-00775-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-020-00775-y
    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/s10463-020-00775-y?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. Jiang, Tiefeng & Wang, Xiangchen & Rao, M. Bhaskara, 1992. "Moderate deviations for some weakly dependent random processes," Statistics & Probability Letters, Elsevier, vol. 15(1), pages 71-76, September.
    2. Burton, Robert M. & Dehling, Herold, 1990. "Large deviations for some weakly dependent random processes," Statistics & Probability Letters, Elsevier, vol. 9(5), pages 397-401, May.
    3. Bryc, Wlodzimierz, 1993. "A remark on the connection between the large deviation principle and the central limit theorem," Statistics & Probability Letters, Elsevier, vol. 18(4), pages 253-256, November.
    4. 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.
    5. 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.
    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. Jiang, Tiefeng & Rao, M. Bhaskara & Wang, Xiangchen, 1995. "Large deviations for moving average processes," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 309-320, October.
    2. Ghosh, Souvik & Samorodnitsky, Gennady, 2009. "The effect of memory on functional large deviations of infinite moving average processes," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 534-561, February.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Wenzhi Yang & Shuhe Hu & Xuejun Wang, 2012. "Complete Convergence for Moving Average Process of Martingale Differences," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-16, July.
    10. 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.
    11. Mele, Angelo, 2013. "Poisson indices of segregation," Regional Science and Urban Economics, Elsevier, vol. 43(1), pages 65-85.
    12. Yun-xia, Li & Li-xin, Zhang, 2004. "Complete moment convergence of moving-average processes under dependence assumptions," Statistics & Probability Letters, Elsevier, vol. 70(3), pages 191-197, December.
    13. Yun-Xia, Li, 2006. "Precise asymptotics in complete moment convergence of moving-average processes," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1305-1315, July.
    14. 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.
    15. Flavio Santi & Maria Michela Dickson & Diego Giuliani & Giuseppe Arbia & Giuseppe Espa, 2021. "Reduced-bias estimation of spatial autoregressive models with incompletely geocoded data," Computational Statistics, Springer, vol. 36(4), pages 2563-2590, December.
    16. Eric Marcon & Florence Puech, 2009. "Generalizing Ripley's K function to inhomogeneous populations," Working Papers halshs-00372631, HAL.
    17. Yannick Useni Sikuzani & Médard Mpanda Mukenza & Héritier Khoji Muteya & Nadège Cirezi Cizungu & François Malaisse & Jan Bogaert, 2023. "Vegetation Fires in the Lubumbashi Charcoal Production Basin (The Democratic Republic of the Congo): Drivers, Extent and Spatiotemporal Dynamics," Land, MDPI, vol. 12(12), pages 1-20, December.
    18. José Ramón González‐Olabarria & Blas Mola‐Yudego & Lluis Coll, 2015. "Different Factors for Different Causes: Analysis of the Spatial Aggregations of Fire Ignitions in Catalonia (Spain)," Risk Analysis, John Wiley & Sons, vol. 35(7), pages 1197-1209, July.
    19. J. S. Marron & S. S. Chung, 2001. "Presentation of smoothers: the family approach," Computational Statistics, Springer, vol. 16(1), pages 195-207, March.
    20. 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.

    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:aistmt:v:73:y:2021:i:5:d:10.1007_s10463-020-00775-y. 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.