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Statistical Methods & Applications

, Volume 24, Issue 2, pp 257–261 | Cite as

Hubert, Rousseeuw and Segaert: multivariate functional outlier detection

  • Aldo Corbellini
  • Marco Riani
  • Anthony C. Atkinson
Discussion
  • 140 Downloads

As would be expected from these authors, this is an interesting and well-written paper. It provides a stimulating introduction to robustness problems in the analysis of functional data. We have four general comments, none extensive.

Robust bivariate boxplots

The “bag-plot” of Rousseeuw et al. (1990), which you exemplify in your Figure 8, provides a polygonal approximation to the unknown distribution. The robust bivariate boxplot introduced by Zani et al. (1998) provides a smoother approximation to the unknown distribution. We briefly recall some of its properties.

Zani et al. (1998) use the peeling of convex hulls to, in the tradition of very robust statistics, find a region that contains approximately 50 % of the data. Peeling of hulls continues until the first one is obtained which includes not more than 50 % of the data (and asymptotically half the data as the sample size increases). The “50 % hull” so found is smoothed using B-splines, with cubic pieces which use the vertices of...

Keywords

Mahalanobis Distance Functional Data Kriging Model Unknown Distribution Functional Data 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.

References

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Aldo Corbellini
    • 1
  • Marco Riani
    • 1
  • Anthony C. Atkinson
    • 2
  1. 1.Dipartimento di EconomiaUniversità di ParmaParmaItaly
  2. 2.Department of StatisticsLondon School of EconomicsLondonUK

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