On a General Definition of Depth for Functional Data

In this paper, we provide an elaboration on the desirable properties of statistical depths for functional data. Although a formal definition has been put forward in the literature, there are still several unclarities to be tackled, and further insights to be gained. Herein, a few interesting connect...

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Veröffentlicht in:Statistical science 2017-11, Vol.32 (4), p.630-639
Hauptverfasser: Gijbels, Irène, Nagy, Stanislav
Format: Artikel
Sprache:eng
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Zusammenfassung:In this paper, we provide an elaboration on the desirable properties of statistical depths for functional data. Although a formal definition has been put forward in the literature, there are still several unclarities to be tackled, and further insights to be gained. Herein, a few interesting connections between the wanted properties are found. In particular, it is demonstrated that the conditions needed for some desirable properties to hold are extremely demanding, and virtually impossible to be met for common depths. We establish adaptations of these properties which prove to be still sensible, and more easily met by common functional depths.
ISSN:0883-4237
2168-8745
DOI:10.1214/17-STS625