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Cokriging for spatial functional data

Author

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  • Nerini, David
  • Monestiez, Pascal
  • Manté, Claude

Abstract

This work proposes to generalize the method of kriging when data are spatially sampled curves. A spatial functional linear model is constructed including spatial dependencies between curves. Under some regularity conditions of the curves, an ordinary kriging system is established in the infinite dimensional case. From a practical point-of-view, the decomposition of the curves into a functional basis boils down the problem of kriging in infinite dimension to a standard cokriging on basis coefficients. The methodological developments are illustrated with temperature profiles sampled with dives of elephant seals in the Antarctic Ocean. The projection of sampled profiles into a Legendre polynomial basis is performed with a regularization procedure based on spline smoothing which uses the variance of the sampling devices in order to estimate coefficients by quadrature.

Suggested Citation

  • Nerini, David & Monestiez, Pascal & Manté, Claude, 2010. "Cokriging for spatial functional data," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 409-418, February.
  • Handle: RePEc:eee:jmvana:v:101:y:2010:i:2:p:409-418
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    References listed on IDEAS

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    1. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
    2. Zhou S. & Shen X., 2001. "Spatially Adaptive Regression Splines and Accurate Knot Selection Schemes," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 247-259, March.
    3. Philippe Besse & J. Ramsay, 1986. "Principal components analysis of sampled functions," Psychometrika, Springer;The Psychometric Society, vol. 51(2), pages 285-311, June.
    4. Pearce, N.D. & Wand, M.P., 2006. "Penalized Splines and Reproducing Kernel Methods," The American Statistician, American Statistical Association, vol. 60, pages 233-240, August.
    5. Meiring, Wendy, 2007. "Oscillations and Time Trends in Stratospheric Ozone Levels: A Functional Data Analysis Approach," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 788-802, September.
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    Citations

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    Cited by:

    1. Martha Bohorquez & Ramón Giraldo & Jorge Mateu, 2016. "Optimal sampling for spatial prediction of functional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(1), pages 39-54, March.
    2. Benhenni, Karim & Su, Yingcai, 2016. "Optimal sampling designs for nonparametric estimation of spatial averages of random fields," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 341-351.
    3. Ruiz-Medina, M.D., 2011. "Spatial autoregressive and moving average Hilbertian processes," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 292-305, February.
    4. Maria Ruiz-Medina & Rosa Espejo & Elvira Romano, 2014. "Spatial functional normal mixed effect approach for curve classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(3), pages 257-285, September.
    5. Menafoglio, Alessandra & Petris, Giovanni, 2016. "Kriging for Hilbert-space valued random fields: The operatorial point of view," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 84-94.
    6. Gromenko, Oleksandr & Kokoszka, Piotr, 2013. "Nonparametric inference in small data sets of spatially indexed curves with application to ionospheric trend determination," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 82-94.
    7. repec:eee:stapro:v:136:y:2018:i:c:p:126-129 is not listed on IDEAS
    8. Menafoglio, Alessandra & Secchi, Piercesare, 2017. "Statistical analysis of complex and spatially dependent data: A review of Object Oriented Spatial Statistics," European Journal of Operational Research, Elsevier, vol. 258(2), pages 401-410.
    9. repec:bla:jorssb:v:79:y:2017:i:1:p:177-196 is not listed on IDEAS
    10. Martha Bohorquez & Ramón Giraldo & Jorge Mateu, 2016. "Optimal sampling for spatial prediction of functional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(1), pages 39-54, March.
    11. Pigoli, Davide & Menafoglio, Alessandra & Secchi, Piercesare, 2016. "Kriging prediction for manifold-valued random fields," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 117-131.

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