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Local Linear M‐estimation in non‐parametric spatial regression

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  • Zhengyan Lin
  • Degui Li
  • Jiti Gao

Abstract

. A robust version of local linear regression smoothers augmented with variable bandwidths is investigated for dependent spatial processes. The (uniform) weak consistency as well as asymptotic normality for the local linear M‐estimator (LLME) of the spatial regression function g(x) are established under some mild conditions. Furthermore, an additive model is considered to avoid the curse of dimensionality for spatial processes and an estimation procedure based on combining the marginal integration technique with LLME is applied in this paper. Meanwhile, we present a simulated study to illustrate the proposed estimation method. Our simulation results show that the estimation method works well numerically.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:30:y:2009:i:3:p:286-314
    DOI: 10.1111/j.1467-9892.2009.00612.x
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    2. Chen, Jia & Li, Degui & Zhang, Lixin, 2010. "Robust estimation in a nonlinear cointegration model," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 706-717, March.
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    6. Hongxia Wang & Jinde Wang & Bo Huang, 2012. "Prediction for spatio-temporal models with autoregression in errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 217-244.

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