Flexible integrated functional depths

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2021-02
Major/Subject
Mcode
Degree programme
Language
en
Pages
29
673-701
Series
Bernoulli, Volume 27, issue 1
Abstract
This paper develops a new class of functional depths. A generic member of this class is coined Jth order kth moment integrated depth. It is based on the distribution of the cross-sectional halfspace depth of a function in the marginal evaluations (in time) of the random process. Asymptotic properties of the proposed depths are provided: we show that they are uniformly consistent and satisfy an inequality related to the law of the iterated logarithm. Moreover, limiting distributions are derived under mild regularity assumptions. The versatility displayed by the new class of depths makes them particularly amenable for capturing important features of functional distributions. This is illustrated in supervised learning, where we show that the corresponding maximum depth classifiers outperform classical competitors.
Description
Keywords
Asymptotics, Data depth, Functional data analysis, Integrated depths, Supervised classification
Other note
Citation
Nagy , S , Helander , S , van Bever , G , Viitasaari , L & Ilmonen , P 2021 , ' Flexible integrated functional depths ' , Bernoulli , vol. 27 , no. 1 , pp. 673-701 . https://doi.org/10.3150/20-BEJ1254