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Bagplots, Boxplots and Outlier Detection for Functional Data

  • Rob Hyndman
  • Han Lin Shang
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

We propose some new tools for visualizing functional data and for identifying functional outliers. The proposed tools make use of robust principal component analysis, data depth and highest density regions. We compare the proposed outlier detection methods with the existing “functional depth” method, and show that our methods have better performance on identifying outliers in French male age-specific mortality data.

Keywords

Functional Data Outlier Detection Principal Component Score High Density Region Robust Principal Component Analysis 
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.

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References

  1. [1]
    Croux, C. & Ruiz-Gazen, A.: High breakdown estimators for principal components: the projection-pursuit approach revisited. Journal of Multivariate Analysis. 95, 206-226 (2003).CrossRefMathSciNetGoogle Scholar
  2. [2]
    Febrero, M., Galeano, P. & González-Manteiga, W.: A functional analysis of NOx levels: location and scale estimation and outlier detection. Computational Statistics. 23 (3),411-427 (2007).CrossRefGoogle Scholar
  3. [3]
    Ferraty, F., & Vieu, P.: Nonparametric Functional Data Analysis. Springer. (2006).Google Scholar
  4. [4]
    Filzmoser, P., Maronna, R. & Werner, M.: Outlier identi cation in high dimensions. Computational Statistics & Data Analysis. 52, 1694-1711 (2008).MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Hall, P.G., Lee, Y. & Park, B.: A method for projecting functional data onto a low-dimensional space. Journal of Computational and Graphical Statistics. 16, 799-812 (2007).CrossRefMathSciNetGoogle Scholar
  6. [6]
    Human Mortality Database, University of California, Berkeley (USA), and Max Planck Institute for Demographical Research (Germany). Viewed 15/4/07, available online at <www.mortality.org> or <www.humanmortality.de>. (2007).
  7. [7]
    Hyndman, R.J.: Computing and graphing highest density regions. The American Statistician. 50(2), 120-126 (1996).CrossRefMathSciNetGoogle Scholar
  8. [8]
    Hyndman, R.J. & Ullah, Md.S.: Robust forecasting of mortality and fertility rates: a functional data approach. Computational Statistics & Data Analysis. 51, 4942-4956 (2007).MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    López-Pintado, S & Romo, J.: Depth-based inference for functional data. Computa-tional Statistics & Data Analysis. 51, 4957-4968 (2007).MATHCrossRefGoogle Scholar
  10. [10]
    Rousseeuw, P., Ruts, I. & Tukey, J.: The bagplot: a bivariate boxplot. The American Statistician. 53(4), 382-387 (1999).CrossRefGoogle Scholar
  11. [11]
    Scott, D. W.: Multivariate density estimation: theory, practice, and visualization. John Wiley and Sons: new York. (1992).MATHCrossRefGoogle Scholar

Copyright information

© Physica-Verlag Heidelberg 2008

Authors and Affiliations

  • Rob Hyndman
    • 1
  • Han Lin Shang
    • 1
  1. 1.Department of Econometrics and Business StatisticsMonash University ClaytonAustralia

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