IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v151y2019icp17-28.html
   My bibliography  Save this article

Large and moderate deviation principles for recursive kernel estimators of a regression function for spatial data defined by stochastic approximation method

Author

Listed:
  • Bouzebda, Salim
  • Slaoui, Yousri

Abstract

In the present paper, we are mainly concerned with a family of kernel type estimators based upon spatial data. More precisely, we establish large and moderate deviations principles for the recursive kernel estimators of a regression function for spatial data defined by the stochastic approximation algorithm.

Suggested Citation

  • Bouzebda, Salim & Slaoui, Yousri, 2019. "Large and moderate deviation principles for recursive kernel estimators of a regression function for spatial data defined by stochastic approximation method," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 17-28.
    • Handle: RePEc:eee:stapro:v:151:y:2019:i:c:p:17-28
    DOI: 10.1016/j.spl.2019.03.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715219300835
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2019.03.007?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. Tran, L. T. & Yakowitz, S., 1993. "Nearest Neighbor Estimators for Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 23-46, January.
    2. Gérard Biau & Benoît Cadre, 2004. "Nonparametric Spatial Prediction," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 327-349, October.
    3. Carbon, Michel & Tran, Lanh Tat & Wu, Berlin, 1997. "Kernel density estimation for random fields (density estimation for random fields)," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 115-125, December.
    4. Tran, Lanh Tat, 1990. "Kernel density estimation on random fields," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 37-53, July.
    5. Zudi Lu & Dag Tjøstheim, 2014. "Nonparametric Estimation of Probability Density Functions for Irregularly Observed Spatial Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1546-1564, December.
    6. Sophie Dabo-Niang & Anne-Françoise Yao, 2013. "Kernel spatial density estimation in infinite dimension space," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(1), pages 19-52, January.
    7. El Machkouri, Mohamed & Volný, Dalibor & Wu, Wei Biao, 2013. "A central limit theorem for stationary random fields," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 1-14.
    8. Puhalskii, A., 1994. "The method of stochastic exponentials for large deviations," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 45-70, November.
    9. Sophie Dabo-Niang & Camille Ternynck & Anne-Françoise Yao, 2016. "Nonparametric prediction of spatial multivariate data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 428-458, June.
    10. Yousri Slaoui, 2015. "Plug-in bandwidth selector for recursive kernel regression estimators defined by stochastic approximation method," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(4), pages 483-509, November.
    11. Al-Sulami, Dawlah & Jiang, Zhenyu & Lu, Zudi & Zhu, Jun, 2017. "Estimation for semiparametric nonlinear regression of irregularly located spatial time-series data," Econometrics and Statistics, Elsevier, vol. 2(C), pages 22-35.
    12. Bouzebda, Salim & Slaoui, Yousri, 2018. "Nonparametric recursive method for kernel-type function estimators for spatial data," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 103-114.
    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. Amiri, Aboubacar & Dabo-Niang, Sophie, 2018. "Density estimation over spatio-temporal data streams," Econometrics and Statistics, Elsevier, vol. 5(C), pages 148-170.
    2. Michel Carbon, 2014. "Histograms for stationary linear random fields," Statistical Inference for Stochastic Processes, Springer, vol. 17(3), pages 245-266, October.
    3. Mohamed El Machkouri, 2011. "Asymptotic normality of the Parzen–Rosenblatt density estimator for strongly mixing random fields," Statistical Inference for Stochastic Processes, Springer, vol. 14(1), pages 73-84, February.
    4. Sophie Dabo-Niang & Anne-Françoise Yao, 2013. "Kernel spatial density estimation in infinite dimension space," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(1), pages 19-52, January.
    5. Li, Linyuan, 2015. "Nonparametric adaptive density estimation on random fields using wavelet method," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 346-355.
    6. Salim Bouzebda & Inass Soukarieh, 2022. "Non-Parametric Conditional U -Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design," Mathematics, MDPI, vol. 11(1), pages 1-69, December.
    7. Ahmad Younso, 2023. "On the consistency of mode estimate for spatially dependent data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(3), pages 343-372, April.
    8. Michel Carbon, 2005. "Frequency Polygons for Random Fields," Working Papers 2005-04, Center for Research in Economics and Statistics.
    9. Biau, Gérard, 2002. "Optimal asymptotic quadratic errors of density estimators on random fields," Statistics & Probability Letters, Elsevier, vol. 60(3), pages 297-307, December.
    10. Sophie Dabo-Niang & Zoulikha Kaid & Ali Laksaci, 2015. "Asymptotic properties of the kernel estimate of spatial conditional mode when the regressor is functional," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(2), pages 131-160, April.
    11. Hongxia Wang & Jinde Wang, 2009. "Estimation of the trend function for spatio-temporal models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(5), pages 567-588.
    12. Rodrigo García Arancibia & Pamela Llop & Mariel Lovatto, 2023. "Nonparametric prediction for univariate spatial data: Methods and applications," Papers in Regional Science, Wiley Blackwell, vol. 102(3), pages 635-672, June.
    13. Michel Carbon, 2008. "Asymptotic Normality of Frequency Polygons for Random Fields," Working Papers 2008-09, Center for Research in Economics and Statistics.
    14. S.‐H. Arnaud Kanga & Ouagnina Hili & Sophie Dabo‐Niang & Assi N'Guessan, 2023. "Asymptotic properties of nonparametric quantile estimation with spatial dependency," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(3), pages 254-283, August.
    15. Kurisu, Daisuke, 2019. "On nonparametric inference for spatial regression models under domain expanding and infill asymptotics," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    16. Liliana Forzani & Ricardo Fraiman & Pamela Llop, 2013. "Density estimation for spatial-temporal models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 321-342, June.
    17. Lee, Y. K. & Choi, H. & Park, B. U. & Yu, K. S., 2004. "Local likelihood density estimation on random fields," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 347-357, July.
    18. Sophie Dabo-Niang & Sidi Ould-Abdi & Ahmedoune Ould-Abdi & Aliou Diop, 2014. "Consistency of a nonparametric conditional mode estimator for random fields," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(1), pages 1-39, March.
    19. Nadia Bensaïd & Sophie Dabo-Niang, 2010. "Frequency polygons for continuous random fields," Statistical Inference for Stochastic Processes, Springer, vol. 13(1), pages 55-80, April.
    20. Dabo-Niang, Sophie & Kaid, Zoulikha & Laksaci, Ali, 2012. "On spatial conditional mode estimation for a functional regressor," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1413-1421.

    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:stapro:v:151:y:2019:i:c:p:17-28. 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.