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Discussion of “Multivariate Functional Outlier Detection”, by Mia Hubert, Peter Rousseeuw and Pieter Segaert

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Abstract

We present a discussion of Hubert et al. (2015)—hereafter, HRS15—that splits into two parts. In the first one, we argue that some structural properties of depth may, in some cases, limit its relevance for outlier detection. We also propose an alternative to bagdistances, which, while still based on depth, does not suffer from the same limitations. In the second part of the discussion, we investigate the possible uses of the weight functions that may enter the various integral functionals considered in HRS15.

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Notes

  1. This can be partly addressed by introducing local versions of depth; see Agostinelli and Romanazzi (2011) and Paindaveine and Van Bever (2013).

  2. A few, isolated, small bagdistances arguably also may be a sign of “outlyingness”.

  3. This is not only the case for shift outliers, but also for shape outliers, provided that the multivariate functional data considered contains derivatives of the original curves.

References

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Authors and Affiliations

  1. Université libre de Bruxelles, Av. F.D. Roosevelt, 50, ECARES - CP114/04, 1050, Brussels, Belgium

    Davy Paindaveine

  2. The Open University, Walton Hall, Milton Keynes, Buckinghamshire, MK7 6AA, UK

    Germain Van Bever

Authors
  1. Davy Paindaveine
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  2. Germain Van Bever
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Corresponding author

Correspondence to Davy Paindaveine.

Additional information

Davy Paindaveine’s research is supported by an A.R.C. contract from the Communauté Française de Belgique and by the IAP research network Grant Nr. P7/06 of the Belgian government (Belgian Science Policy). Germain Van Bever’s research is supported by the British EPSRC grant EP/L010419/1.

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Paindaveine, D., Van Bever, G. Discussion of “Multivariate Functional Outlier Detection”, by Mia Hubert, Peter Rousseeuw and Pieter Segaert. Stat Methods Appl 24, 223–231 (2015). https://doi.org/10.1007/s10260-015-0307-x

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