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-estimation for spatial nonparametric regression

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  • Rongrong Xu
  • Jinde Wang

Abstract

Assuming the structure of a mixing spatial data process {(Yi, Xi), i∈ℝN}, the least absolute deviation (L1) method is proposed to estimate the spatial conditional regression function with the superiority of weakening the influence of outliers and aberrant observations, which appear very often in spatial data. With appropriate choices of the bandwidth under some mild conditions imposed on the spatial process, the asymptotic distributions of the estimators are derived. Three simulation models using L1 and L2 methods respectively show that the L1-estimators are superior to L2-estimators.

Suggested Citation

  • Rongrong Xu & Jinde Wang, 2008. "-estimation for spatial nonparametric regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(6), pages 523-537.
    • Handle: RePEc:taf:gnstxx:v:20:y:2008:i:6:p:523-537
    DOI: 10.1080/10485250801976717
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    References listed on IDEAS

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    1. Hallin, Marc & Lu, Zudi & Tran, Lanh T., 2004. "Kernel density estimation for spatial processes: the L1 theory," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 61-75, January.
    2. Gérard Biau & Benoît Cadre, 2004. "Nonparametric Spatial Prediction," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 327-349, October.
    3. Wang, J. D., 1995. "Asymptotic Normality of L1-Estimators in Nonlinear Regression," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 227-238, August.
    4. Marc Hallin & Zudi Lu & Lanh T. Tran, 2004. "Local linear spatial regression," ULB Institutional Repository 2013/2131, ULB -- Universite Libre de Bruxelles.
    5. Lu, Zudi & Chen, Xing, 2004. "Spatial kernel regression estimation: weak consistency," Statistics & Probability Letters, Elsevier, vol. 68(2), pages 125-136, June.
    6. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
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