¹Universidad Nacional de Colombia, Sciences Faculty, Department of Statistics, Bogotá, Colombia. Associate professor. Email: rgiraldoh@unal.edu.co
²Universitat Jaume I, Department of Mathematics, Castellón, Spain. Professor. Email: mateu@mat.uji.es
³Universitat Politècnica de Catalunya, Department of Statistics and Operations Research, Barcelona, Spain. Associate professor. Email: pedro.delicado@upc.edu

Spatially correlated curves are present in a wide range of applied disciplines. In this paper we describe the R package geofd which implements ordinary kriging prediction for this type of data. Initially the curves are pre-processed by fitting a Fourier or B-splines basis functions. After that the spatial dependence among curves is estimated by means of the trace-variogram function. Finally the parameters for performing prediction by ordinary kriging at unsampled locations are by estimated solving a linear system based estimated trace-variogram. We illustrate the software analyzing real and simulated data.

Key words: Functional data, Smoothing, Spatial data, Variogram.

Curvas espacialmente correlacionadas están presentes en un amplio rango de disciplinas aplicadas. En este trabajo se describe el paquete R geofd que implementa predicción por kriging ordinario para este tipo de datos. Inicialmente las curvas son suavizadas usando bases de funciones de Fourier o B-splines. Posteriormente la dependencia espacial entre las curvas es estimada por la función traza-variograma. Finalmente los parámetros del predictor kriging ordinario son estimados resolviendo un sistema de ecuaciones basado en la estimación de la función traza-variograma. Se ilustra el paquete analizando datos reales y simulados.

Palabras clave: datos funcionales, datos espaciales, suavizado, variograma.

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References

1. Baladandayuthapani, V., Mallick, B., Hong, M., Lupton, J., Turner, N. & Caroll, R. (2008), 'Bayesian hierarchical spatially correlated functional data analysis with application to colon carcinoginesis', Biometrics 64, 64-73.         [ Links ]

2. Box, G. & Jenkins, G. (1976), Time Series Analysis., Holden Day, New York.         [ Links ]

3. Cressie, N. (1993), Statistics for Spatial Data, John Wiley & Sons, New York.         [ Links ]

4. Cuevas, A., Febrero, M. & Fraiman, R. (2004), 'An ANOVA test for functional data.', Computational Statistics and Data Analysis 47, 111-122.         [ Links ]

5. Delicado, P., Giraldo, R., Comas, C. & Mateu, J. (2010), 'Statistics for spatial functional data: some recent contributions', Environmetrics 21, 224-239.         [ Links ]

6. Ferraty, F. & Vieu, P. (2006), Nonparametric Functional Data Analysis. Theory and Practice, Springer, New York.         [ Links ]

7. Giraldo, R. (2009), Geostatistical Analysis of Functional Data, PhD thesis, Universitat Politècnica de Catalunya.         [ Links ]

8. Giraldo, R., Delicado, P. & Mateu, J. (2010), 'Continuous time-varying kriging for spatial prediction of functional data: an environmental application', Journal of Agricultural, Biological, and Environmental Statistics 15(1), 66-82.         [ Links ]

9. Giraldo, R., Delicado, P. & Mateu, J. (2011), 'Ordinary kriging for function-valued spatial data', Environmental and Ecological Statistics 18(3), 411-426.         [ Links ]

10. Goulard, M. & Voltz, M. (1993), Geostatistical interpolation of curves: a case study in soil science, 'Geostatistics Tróia 92', Vol. 2, Kluwer Academc Press, p. 805-816.         [ Links ]

11. Grosjean, P. (2010), SciViews-R: A GUI API for R, UMONS, Mons, Belgium. *http://www.sciviews.org/SciViews-R         [ Links ]

12. MATLAB, (2010), version 7.10.0 (R2010a), The MathWorks Inc., Natick, Massachusetts.         [ Links ]

13. Malfait, N. & Ramsay, J. (2003), 'The historical functional linear model', The Canadian Journal of Statistics 31(2), 115-128.         [ Links ]

14. Myers, D. (1982), 'Matrix formulation of co-kriging', Mathematical Geology 14(3), 249-257.         [ Links ]

15. Nerini, D., Monestiez, P. & Manté, C. (2010), 'Cokriging for spatial functional data', Journal of Multivariate Analysis 101(2), 409-418.         [ Links ]

16. Ramsay, J., Hooker, G. & Graves, S. (2009), Functional Data Analysis with R and MATLAB, Springer, New York.         [ Links ]

17. Ramsay, J. & Silverman, B. (2005), Functional Data Analysis. Second edition, Springer, New York.         [ Links ]

18. Ramsay, J., Wickham, H., Graves, S. & Hooker, G. (2010), fda: Functional Data Analysis. R package version 2.2.6. *http://cran.r-project.org/web/packages/fda         [ Links ]

19. Ribeiro, P. & Diggle, P. (2001), 'GeoR: a package for geostatistical analysis', R-NEWS 1(2), 15-18. *http://cran.R-project.org/doc/Rnews         [ Links ]

20. R Development Core Team, (2011), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. *http://www.R-project.org.         [ Links ]

21. Staicu, A., Crainiceanu, C. & Carroll, R. (2010), 'Fast methods for spatially correlated multilevel functional data', Biostatistics 11(2), 177-194.         [ Links ]

22. Ver Hoef, J. & Cressie, N. (1993), 'Multivariable spatial prediction', Mathematical Geology 25(2), 219-240.         [ Links ]

23. Wackernagel, H. (1995), Multivariate Geostatistics: An Introduction with Applications, Springer-Verlag, Berlin.         [ Links ]

24. Yamanishi, Y. & Tanaka, Y. (2003), 'Geographically weighted functional multiple regression analysis: a numerical investigation', Journal of Japanese Society of Computational Statistics 15, 307-317.         [ Links ]

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