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November 2017 On a General Definition of Depth for Functional Data
Irène Gijbels, Stanislav Nagy
Statist. Sci. 32(4): 630-639 (November 2017). DOI: 10.1214/17-STS625


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.


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Irène Gijbels. Stanislav Nagy. "On a General Definition of Depth for Functional Data." Statist. Sci. 32 (4) 630 - 639, November 2017.


Published: November 2017
First available in Project Euclid: 28 November 2017

zbMATH: 1381.62098
MathSciNet: MR3730526
Digital Object Identifier: 10.1214/17-STS625

Keywords: data depth , functional data , multivariate statistics , robustness

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.32 • No. 4 • November 2017
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