Outlier Detection for Geostatistical Functional Data: An Application to Sensor Data

Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

In this paper we propose an outlier detection method for geostatistical functional data. Our approach generalizes the functional proposal of Febrero et al. (Comput 5 Stat 22(3):411–427, 2007; Environmetrics 19(4):331–345, 2008) in the spatial framework. It is based on the concept of the kernelized functional modal depth that we have opportunely defined extending the functional modal depth. As an illustration, the methodology is applied to sensor data corresponding to long-term daily climatic time series from meteorological stations.

Keywords

Depth Function Functional Data Outlier Detection Functional Data Analysis Functional Context 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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.MathSciNetMATHCrossRefGoogle Scholar
  2. Cressie, N. (1993). Statistics for spatial data. New York: Wiley.Google Scholar
  3. Cuevas, A., Febrero, M., & Fraiman, R. (2006). On the use of bootstrap for estimating functions with functional data. Computational Statistics and Data Analysis, 51, 1063–1074.MathSciNetMATHCrossRefGoogle Scholar
  4. Cuevas, A., Febrero, M., & Fraiman, R. (2007). Robust estimation and classification for functional data via projection-based depth notions. Computational Statistics, 22, 481–496. doi:10.1007/s00180-007-0053-0.MathSciNetMATHCrossRefGoogle Scholar
  5. Delicado, P., Giraldo, R., Comas, C., & Mateu, J. (2010). Statistics for spatial functional data: Some recent contributions. Environmetrics, 21, 224–239.MathSciNetCrossRefGoogle Scholar
  6. Febrero, M., Galeano, P., & Gonzalez-Manteiga, W. (2007). Functional analysis of NOx levels: Location and scale estimation and outlier detection. Computational Statistics, 22(3), 411–427.MathSciNetMATHCrossRefGoogle Scholar
  7. Febrero, M., Galeano, P., & Gonzalez-Manteiga, W. (2008). Outlier detection in functional data by depth measures, with application to identify abnormal NOx levels. Environmetrics, 19(4), 331–345.MathSciNetCrossRefGoogle Scholar
  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 (JABES), 15, 66–82.Google Scholar
  9. Giraldo, R., Delicado, P., & Mateu, J. (2011). Ordinary kriging for function-valued spatial data. Environmental and Ecological Statistics, 18, 411–426. doi:10.1007/s10651-010-0143-yMathSciNetCrossRefGoogle Scholar
  10. Giraldo, R., Delicado, P., & Mateu, J. (2012). Hierarchical clustering of spatially correlated functional data. Statistica Neerlandica. doi:10.1111/j.1467-9574.2012.00522.xGoogle Scholar
  11. Giraldo, R., & Mateu, J. (2012). Kriging for functional data. In Encyclopedia of Environmetrics, (2nd ed.). ForthcomingGoogle Scholar
  12. Hawkins, D. M. (1980). Identification of outliers. London: Chapman and Hall.MATHGoogle Scholar
  13. Hyndman, R. J., & Shang, H. L. (2010). Rainbow plots, bagplots, and boxplots for functional data. Journal of Computational and Graphical Statistics, 19, 29–45.MathSciNetCrossRefGoogle Scholar
  14. Nerini, D., & Monestiez, P. (2008). A cokriging method for spatial functional data With applications in oceanology. Long summary sent to “The First International Workshop on Functional and Operational Statistics”, Toulouse.Google Scholar
  15. Nerini, D., Monestiez, P., & Manté, C. (2010). A cokriging method for spatial functional. Journal of Multivariate Analysis, 101, 409–418.MathSciNetMATHCrossRefGoogle Scholar
  16. Ramsay, J. E., & Silverman, B. W. (2005). Functional data analysis (2nd ed.). Springer: New York.Google Scholar
  17. Romano, E., Balzanella, A., & Verde, R. (2010). A regionalization method for spatial functional data based on variogram models: An application on environmental data. In Proceedings of the 45th Scientific Meeting of the Italian Statistical Society, Padova.Google Scholar
  18. Sun, Y., & Genton, M. G. (2011). Functional boxplots. Journal of Computational and Graphical Statistics, 20, 316–334.MathSciNetCrossRefGoogle Scholar
  19. Sun, Y., & Genton, M. G. (2012). Adjusted functional boxplots for spatio-temporal data visualization and outlier detection. Environmetrics, 23, 54–64.MathSciNetCrossRefGoogle Scholar
  20. Yamanishi, Y., & Tanaka, Y. (2003). Geographically weighted functional multiple regression analysis: A numerical investigation. Journal of Japanese Society of Computational Statistics, 15, 307–317.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Dipartimento di Studi Europei e MediterraneiSeconda Università degli Studi di NapoliNapoliItaly
  2. 2.Departamento de MatematicasUniversitat Jaume ICastellon de la PlanaSpain

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