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Journal of Mathematical Modelling and Algorithms

, Volume 4, Issue 3, pp 237–252 | Cite as

Variography for Model Selection in Local Polynomial Regression with Spatial Data

  • J. M. MatíasEmail author
  • W. González-Manteiga
  • M. Francisco-Fernández
  • C. Ordóñez
Research Article
  • 68 Downloads

Abstract

In this work, we apply variographic techniques from spatial statistics to the problem of model selection in local polynomial regression with multivariate data. These techniques permit selection of the kernel and smoothing matrix with less computational load and interpretation of the regularity of the regression function in different directions. Moreover, they may represent the only feasible alternative for problems of a certain dimensionality.

Key words

local polynomial regression model selection bandwidth matrix kernels variography spatial statistics 

Mathematical Subject Classification (2000)

62G08 62H11 65C60 86A32 91B72 

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References

  1. 1.
    Cressie, N.: Statistics for Spatial Data, Wiley, 1993.Google Scholar
  2. 2.
    Fan, J. and Gijbels, I.: Local Polynomial Modeling and Its Applications, Chapman & Hall, 1996.Google Scholar
  3. 3.
    Francisco-Fernandez, M. and Opsomer, J. D.: Smoothing parameter selection methods for nonparametric regression with spatially correlated errors, in: Proceedings of the ISI International Conference, Universidad de Santiago de Compostela, Spain, 2003.Google Scholar
  4. 4.
    Hart, J.: Some automated methods of smoothing time-dependent data, Nonparametr. Statist. 6 (1996), 115–142.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Journel, A. G. and Huijbregts, C. J.: Mining Geostatistics, Academic, 1978.Google Scholar
  6. 6.
    Kent, J. T.: Continuity properties for random fields, Ann. Probab. 17 (1989), 1432–1440.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Matias, J. M., Vaamonde, A., Taboada, J., and Gonzalez-Manteiga, W.: Comparison between kriging and neural networks with application to the exploitation of a slate mine, Math. Geol. 36 (2004), 485–508.CrossRefGoogle Scholar
  8. 8.
    Matias, J. M., Vaamonde, A., Taboada, J., and Gonzalez-Manteiga, W.: Support vector machines and gradient boosting for graphical estimation of a slate deposit, J. Stoch. Environ. Res. Risk Assess. 18 (2004), 309–323.CrossRefzbMATHGoogle Scholar
  9. 9.
    Opsomer, J. D., Wang, Y., and Yang, Y.: Non parametric regression with correlated errors, Stat. Sci. 16 (2001), 134–153.CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Stein, M.: Interporlation of Spatial Data: Some Theory for Kriging, Springer, 1999.Google Scholar
  11. 11.
    Taboada, J., Saavedra, A., and Vaamonde, A.: Evaluation of a slate extraction bank, Trans. Inst. Min. Metall., A, 110 (2001) 40–46.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • J. M. Matías
    • 1
    • 4
    Email author
  • W. González-Manteiga
    • 2
  • M. Francisco-Fernández
    • 3
  • C. Ordóñez
    • 1
  1. 1.University of VigoVigoSpain
  2. 2.University of Santiago de CompostelaSantiago de CompostelaSpain
  3. 3.University of La CoruñaLa CoruñaSpain
  4. 4.Depto. de Ingegneria de los Recursos, de Naturales y Medio AmbienteETS de Ingenieros de MinasMadridVigoSpain

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