Hubert, Rousseeuw and Segaert: multivariate functional outlier detection
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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...
KeywordsMahalanobis Distance Functional Data Kriging Model Unknown Distribution Functional Data Analysis
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