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B-spline estimation for spatial data

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  • Tang Qingguo
  • Cheng Longsheng

Abstract

Data collected on the surface of the earth often have spatial interaction. In this paper, a global smoothing procedure is developed using a tensor product of B-spline function approximations for estimating the spatial multi-dimensional conditional regression function. Under mild regularity assumptions, the global convergence rates of the B-spline estimators are established. Asymptotic results show that our B-spline estimators achieve the optimal convergence rate. The asymptotic normality of our estimator is also derived. Finite sample properties of our procedures are studied through Monte Carlo simulations.

Suggested Citation

  • Tang Qingguo & Cheng Longsheng, 2010. "B-spline estimation for spatial data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 197-217.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:2:p:197-217
    DOI: 10.1080/10485250903272569
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    References listed on IDEAS

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    1. Gao, Jiti & Lu, Zudi & Tjostheim, Dag, 2003. "Estimation in semiparametric spatial regression," MPRA Paper 11971, University Library of Munich, Germany.
    2. Marc Hallin & Lanh T. Tran, 1996. "Kernel density estimation for linear processes: asymptotic normality and bandwidth selection," ULB Institutional Repository 2013/2055, ULB -- Universite Libre de Bruxelles.
    3. Marc Hallin & Lanh Tran, 1996. "Kernel density estimation for linear processes: Asymptotic normality and optimal bandwidth derivation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(3), pages 429-449, September.
    4. Tang Qingguo & Cheng Longsheng, 2008. "M-estimation and B-spline approximation for varying coefficient models with longitudinal data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(7), pages 611-625.
    5. Lu, Zudi & Lundervold, Arvid & Tjøstheim, Dag & Yao, Qiwei, 2007. "Exploring spatial nonlinearity using additive approximation," LSE Research Online Documents on Economics 5401, London School of Economics and Political Science, LSE Library.
    6. 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.
    7. Jianhua Z. Huang & Haipeng Shen, 2004. "Functional Coefficient Regression Models for Non‐linear Time Series: A Polynomial Spline Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 515-534, December.
    8. Tran, L. T. & Yakowitz, S., 1993. "Nearest Neighbor Estimators for Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 23-46, January.
    9. Marc Hallin & Zudi Lu & Lanh T. Tran, 2001. "Density estimation for spatial linear processes," ULB Institutional Repository 2013/2109, ULB -- Universite Libre de Bruxelles.
    10. Tran, Lanh Tat, 1990. "Kernel density estimation on random fields," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 37-53, July.
    11. Marc Hallin & Zudi Lu & Lanh T. Tran, 2004. "Local linear spatial regression," ULB Institutional Repository 2013/2131, ULB -- Universite Libre de Bruxelles.
    12. Xuming He, 2002. "Estimation in a semiparametric model for longitudinal data with unspecified dependence structure," Biometrika, Biometrika Trust, vol. 89(3), pages 579-590, August.
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