IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v68y2004i2p125-136.html
   My bibliography  Save this article

Spatial kernel regression estimation: weak consistency

Author

Listed:
  • Lu, Zudi
  • Chen, Xing

Abstract

In this paper, we introduce a kernel method to estimate a spatial conditional regression under mixing spatial processes. Some preliminary statistical properties including weak consistency and convergence rates are investigated. The sufficient conditions on mixing coefficients and the bandwidth are established to ensure distribution-free weak consistency, which requires no assumption on the regressor and allows the mixing coefficients decreasing to zero slowly. However, to achieve an optimal convergence rate, some requirements on the regressor and the decreasing rate of mixing coefficients tending to zero are needed.

Suggested Citation

  • Lu, Zudi & Chen, Xing, 2004. "Spatial kernel regression estimation: weak consistency," Statistics & Probability Letters, Elsevier, vol. 68(2), pages 125-136, June.
    • Handle: RePEc:eee:stapro:v:68:y:2004:i:2:p:125-136
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(03)00291-8
    Download Restriction: Full text for ScienceDirect subscribers only

    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, Lanh Tat, 1990. "Kernel density estimation on random fields," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 37-53, July.
    2. Masry, Elias & Györfi, László, 1987. "Strong consistency and rates for recursive probability density estimators of stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 22(1), pages 79-93, June.
    3. Tran, L. T. & Yakowitz, S., 1993. "Nearest Neighbor Estimators for Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 23-46, January.
    4. Kulkarni, P. M., 1992. "Estimation of parameters of a two-dimensional spatial autoregressive model with regression," Statistics & Probability Letters, Elsevier, vol. 15(2), pages 157-162, September.
    5. Marc Hallin & Michel Carbon & Lanh T. Tran, 1996. "Kernel density estimation on random fields: the L1 theory," ULB Institutional Repository 2013/2065, ULB -- Universite Libre de Bruxelles.
    6. Marc Hallin & Zudi Lu & Lanh T. Tran, 2001. "Density estimation for spatial linear processes," ULB Institutional Repository 2013/2109, ULB -- Universite Libre de Bruxelles.
    7. Boente, Graciela & Fraiman, Ricardo, 1988. "Consistency of a nonparametric estimate of a density function for dependent variables," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 90-99, April.
    8. Ioannides, D. & Roussas, G. G., 1987. "Note on the uniform convergence of density estimates for mixing random variables," Statistics & Probability Letters, Elsevier, vol. 5(4), pages 279-285, June.
    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. Jenish, Nazgul, 2012. "Nonparametric spatial regression under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 167(1), pages 224-239.
    2. Jia Chen & Li-Xin Zhang, 2010. "Local linear M-estimation for spatial processes in fixed-design models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(3), pages 319-340, May.
    3. Zhengyan Lin & Degui Li & Jiti Gao, 2009. "Local Linear M-estimation in non-parametric spatial regression," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(3), pages 286-314, May.
    4. Gao, Jiti & Lu, Zudi & Tjostheim, Dag, 2003. "Estimation in semiparametric spatial regression," MPRA Paper 11971, University Library of Munich, Germany.
    5. 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.
    6. repec:spr:stpapr:v:58:y:2017:i:4:d:10.1007_s00362-015-0735-6 is not listed on IDEAS
    7. Tang Qingguo, 2015. "Robust estimation for spatial semiparametric varying coefficient partially linear regression," Statistical Papers, Springer, vol. 56(4), pages 1137-1161, November.
    8. El Machkouri, Mohamed & Es-Sebaiy, Khalifa & Ouassou, Idir, 2017. "On local linear regression for strongly mixing random fields," Journal of Multivariate Analysis, Elsevier, vol. 156(C), pages 103-115.
    9. 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.
    10. 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.
    11. Chen Jia & Zhang Lixin & Li Degui, 2008. "Spatial local M-estimation under association," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(1), pages 11-29, January.

    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:68:y:2004:i:2:p:125-136. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.