@article{2196729fd4b44f34a869c4c7a3216647,
title = "Flexible integrated functional depths",
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.",
keywords = "Asymptotics, Data depth, Functional data analysis, Integrated depths, Supervised classification",
author = "{Van Bever}, Germain and Pauliina Ilmonen and Stanislav Nagy and Sami Helander and Lauri Viitasaari",
note = "Funding Information: The authors greatly appreciate the insightful comments of an Associate Editor and a referee, which led to distinct improvements in the paper. The authors would also like to acknowledge the computational resources provided by the Aalto University School of Science ?Science-IT? project. S. Nagy wishes to thank the Czech Science Foundation (grant 19-16097Y) and Charles University (grant PRIMUS/17/SCI/3). G. Van Bever would like to thank the Belgian FNRS (grant Cr?dit de recherche C 60/5?CDR/OL). P. Ilmonen and L. Viitasaari wish to thank the V?is?l? foundation for its support. Funding Information: The authors greatly appreciate the insightful comments of an Associate Editor and a referee, which led to distinct improvements in the paper. The authors would also like to acknowledge the computational resources provided by the Aalto University School of Science “Science-IT” project. S. Nagy wishes to thank the Czech Science Foundation (grant 19-16097Y) and Charles University (grant PRIMUS/17/SCI/3). G. Van Bever would like to thank the Belgian FNRS (grant Cr{\'e}dit de recherche C 60/5–CDR/OL). P. Ilmonen and L. Viitasaari wish to thank the V{\"a}is{\"a}l{\"a} foundation for its support. Publisher Copyright: {\textcopyright} 2021 ISI/BS.",
year = "2021",
month = feb,
doi = "10.3150/20-BEJ1254",
language = "English",
volume = "27",
pages = "673--701",
journal = "Bernoulli : a journal of mathematical statistics and probability",
issn = "1350-7265",
publisher = "International Statistical Institute",
number = "1",
}