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February 2021 Flexible integrated functional depths
Stanislav Nagy, Sami Helander, Germain Van Bever, Lauri Viitasaari, Pauliina Ilmonen
Bernoulli 27(1): 673-701 (February 2021). DOI: 10.3150/20-BEJ1254

Abstract

This paper develops a new class of functional depths. A generic member of this class is coined $J$th order $k$th 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.

Citation

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Stanislav Nagy. Sami Helander. Germain Van Bever. Lauri Viitasaari. Pauliina Ilmonen. "Flexible integrated functional depths." Bernoulli 27 (1) 673 - 701, February 2021. https://doi.org/10.3150/20-BEJ1254

Information

Received: 1 November 2019; Revised: 1 March 2020; Published: February 2021
First available in Project Euclid: 20 November 2020

zbMATH: 07282866
MathSciNet: MR4177385
Digital Object Identifier: 10.3150/20-BEJ1254

Rights: Copyright © 2021 Bernoulli Society for Mathematical Statistics and Probability

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Vol.27 • No. 1 • February 2021
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